Invariants Under Tori Of Rings Of Differential Operators And Related Topics
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Invariants Under Tori Of Rings Of Differential Operators And Related Topics
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Author : Ian Malcolm Musson
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Invariants Under Tori Of Rings Of Differential Operators And Related Topics written by Ian Malcolm Musson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X) $ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k \times (k ) $. They give a precise description of the primitive ideals in $D(X) $ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X) $. The latter are of the form $B =D(X) /({\germ g}-\chi({\germ g}))$ where ${\germ g}= {\rm Lie}(G)$, $\chi\in {\germ g} ast$ and ${\germ g}-\chi({\germ g})$ is the set of all $v-\chi(v)$ with $v\in {\germ g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X/\!/G)$ is a simple ring.
Continuous Tensor Products And Arveson S Spectral C Algebras
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Author : Joachim Zacharias
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Continuous Tensor Products And Arveson S Spectral C Algebras written by Joachim Zacharias and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in operator algebras
The Spectrum Of A Module Category
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Author : Henning Krause
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
The Spectrum Of A Module Category written by Henning Krause and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
These notes present an introduction into the spectrum of the category of modules over a ring. We discuss the general theory of pure-injective modules and concentrate on the isomorphism classes of indecomposable pure-injective modules which form the underlying set of this spectrum. The interplay between the spectrum and the category of finitely presented modules provides new insight into the geometrical and homological properties of the category of finitely presented modules. Various applications from representation theory of finite dimensional algebras are included.
Squared Hopf Algebras
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Author : Volodymyr V. Lyubashenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Squared Hopf Algebras written by Volodymyr V. Lyubashenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is intended for graduate students and research mathematicians interested in associative rings and algebras.
Black Box Classical Groups
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Author : William M. Kantor
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Black Box Classical Groups written by William M. Kantor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimensional unitary group.
Rational Homotopical Models And Uniqueness
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Author : Martin Majewski
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Rational Homotopical Models And Uniqueness written by Martin Majewski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The main goal of this paper is to prove the following conjecture of Baues and Lemaire: the differential graded Lie Tlgebra associated with the Sullivan model of a space is homotopy equivalent to its Quillen model. In addition we show the same for the cellular Lie algebra model which we build from the simplicial analog of the classical Adams-Hilton model. It turns out that this cellular Lie algebra model is one link in a chain of models connecting the models of Quillen and Sullivan.The key result which makes all this possible is Anick's correspondence between differential graded Lie algebras and Hopf algebras up to homotopy. In addition we show that the Quillen model is a rational homotopical equivalence, and we conclude the same for the other models using our main result. Theconstruction of the three models is given in detail. The background from homotopy theory, differential algebra, and algebra is presented in great generality.
Non Additive Exact Functors And Tensor Induction For Mackey Functors
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Author : Serge Bouc
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Non Additive Exact Functors And Tensor Induction For Mackey Functors written by Serge Bouc and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
First the author introduces a generalization of the notion of (right)-exact functor between abelian categories to the case of non-additive functors. The main result of this section is an extension theorem: any functor defined on a suitable subcategory can be extended uniquely to a right exact functor defined on the whole category. Next those results are used to define various functors of generalized tensor induction, associated to finite bisets, between categories attached to finite groups. This includes a definition of tensor induction for Mackey functors, for cohomological Mackey functors, for p-permutation modules and algebras. This also gives a single formalism of bisets for restriction, inflation, and ordinary tensor induction for modules.
Homogeneous Integral Table Algebras Of Degree Three A Trilogy
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Author : Harvey I. Blau
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Homogeneous Integral Table Algebras Of Degree Three A Trilogy written by Harvey I. Blau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three. On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism oforder three. Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.
Quantum Linear Groups And Representations Of Gl N Mathbb F Q
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Author : Jonathan Brundan
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Quantum Linear Groups And Representations Of Gl N Mathbb F Q written by Jonathan Brundan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts, such as the computation of decomposition numbers and blocks of GL[n(F[q) from knowledge of the same for the quantum group, and the non-defining analogue of Steinberg's tensor product theorem. We also easily obtain a new double centralizer property between GL[n(F[[q) and quantum GL[n, generalizing a result of Takeuchi. Finally, we apply the theory to study the affine general linear group, following ideas of Zelevinsky in characteristic zero. We prove results that can be regarded as the modular analogues of Zelevinsky's and Thoma's branching rules. Using these, we obtain a new dimension formula for the irreducible cross-characteristic representations of GL[n(F[q), expressing their dimensions in terms of the characters of irreducible modules over the quantum group.
Annihilating Fields Of Standard Modules Of Mathfrak Sl 2 Mathbb C Sim And Combinatorial Identities
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Author : Arne Meurman
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Annihilating Fields Of Standard Modules Of Mathfrak Sl 2 Mathbb C Sim And Combinatorial Identities written by Arne Meurman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\frak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\frak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\frak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\frak g}$ is of type $A{(1)} 1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.