The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality written by K. R. Goodearl 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 2005 with Mathematics categories.
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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Author : Friedrich Wehrung
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality written by Friedrich Wehrung 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 2005 with Boolean rings categories.
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality
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Author : K. R. Goodearl
language : en
Publisher:
Release Date : 2014-09-11
The Complete Dimension Theory Of Partially Ordered Systems With Equivalence And Orthogonality written by K. R. Goodearl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Boolean rings categories.
Introduction Partial commutative monoids Continuous dimension scales Espaliers Classes of espaliers Bibliography Index
Ramanujan S Forty Identities For The Rogers Ramanujan Functions
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Ramanujan S Forty Identities For The Rogers Ramanujan Functions written by Bruce C. Berndt 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 2007 with Mathematics categories.
Sir Arthur Conan Doyle's famous fictional detective Sherlock Holmes and his sidekick Dr. Watson go camping and pitch their tent under the stars. During the night, Holmes wakes his companion and says, ``Watson, look up at the stars and tell me what you deduce.'' Watson says, ``I see millions of stars, and it is quite likely that a few of them are planets just like Earth. Therefore there may also be life on these planets.'' Holmes replies, ``Watson, you idiot. Somebody stole ourtent.'' When seeking proofs of Ramanujan's identities for the Rogers-Ramanujan functions, Watson, i.e., G. N. Watson, was not an ``idiot.'' He, L. J. Rogers, and D. M. Bressoud found proofs for several of the identities. A. J. F. Biagioli devised proofs for most (but not all) of the remaining identities.Although some of the proofs of Watson, Rogers, and Bressoud are likely in the spirit of those found by Ramanujan, those of Biagioli are not. in particular, Biagioli used the theory of modular forms. Haunted by the fact that little progress has been made into Ramanujan's insights on these identities in the past 85 years, the present authors sought ``more natural'' proofs. Thus, instead of a missing tent, we have had missing proofs, i.e., Ramanujan's missing proofs of his forty identities for theRogers-Ramanujan functions. in this paper, for 35 of the 40 identities, the authors offer proofs that are in the spirit of Ramanujan. Some of the proofs presented here are due to Watson, Rogers, and Bressoud, but most are new. Moreover, for several identities, the authors present two or threeproofs. For the five identities that they are unable to prove, they provide non-rigorous verifications based on an asymptotic analysis of the associated Rogers-Ramanujan functions. This method, which is related to the 5-dissection of the generating function for cranks found in Ramanujan's lost notebook, is what Ramanujan might have used to discover several of the more difficult identities. Some of the new methods in this paper can be employed to establish new identities for the Rogers-Ramanujanfunctions.
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension
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Author : Sonia Natale
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension written by Sonia Natale 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 2007 with Mathematics categories.
The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.
Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations
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Author : Greg Hjorth
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations written by Greg Hjorth 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 2005 with Mathematics categories.
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.
Lax Phillips Scattering And Conservative Linear Systems A Cuntz Algebra Multidimensional Setting
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Author : Joseph A. Ball
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Lax Phillips Scattering And Conservative Linear Systems A Cuntz Algebra Multidimensional Setting written by Joseph A. Ball 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 2005 with Mathematics categories.
The evolution operator for the Lax-Phillips scattering system is an isometric representation of the Cuntz algebra, while the nonnegative time axis for the conservative, linear system is the free semigroup on $d$ letters. This title presents a multivariable setting for Lax-Phillips scattering and for conservative, discrete-time, linear systems.
Homological And Homotopical Aspects Of Torsion Theories
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Author : Apostolos Beligiannis
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Homological And Homotopical Aspects Of Torsion Theories written by Apostolos Beligiannis 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 2007 with Mathematics categories.
In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and moregenerally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand,and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along theselines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.
Equivalences Of Classifying Spaces Completed At The Prime Two
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Author : Robert Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Equivalences Of Classifying Spaces Completed At The Prime Two written by Robert Oliver 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 2006 with Mathematics categories.
We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.
The Beilinson Complex And Canonical Rings Of Irregular Surfaces
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Author : Alberto Canonaco
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
The Beilinson Complex And Canonical Rings Of Irregular Surfaces written by Alberto Canonaco 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 2006 with Mathematics categories.
An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P n$ in terms of the vector bundles $\Omega {\mathbb{P n j(j)$ for $0\le j\le n$. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on $\mathbb{P ({\rm w )$ (the weighted projective space of weights $\rm w=({\rm w 0,\dots,{\rm w n)$), a suitable category of graded coherent sheaves (the two categories are equivalent if and only if ${\rm w 0=\cdots={\rm w n=1$, i.e. $\mathbb{P ({\rm w )= \mathbb{P n$), obtained by endowing $\mathbb{P ({\rm w )$ with a natural graded structure sheaf. The resulting graded ringed space $\overline{\mathbb{P ({\rm w )$ is an example of graded scheme (in chapter 1 graded schemes are defined and studied in some greater generality than is needed in the rest of the work). Then in chapter 2 we prove This weighted version of Beilinson's theorem is then applied in chapter 3 to prove a structure theorem for good birational weighted canonical projections of surfaces of general type (i.e., for morphisms, which are birational onto the image, from a minimal surface of general type $S$ into a $3$-dimensional $\mathbb{P ({\rm w )$, induced by $4$ sections $\sigma i\in H0(S,\mathcal{O S({\rm w iK S))$). This is a generalization of a theorem by Catanese and Schreyer (who treated the case of projections into $\mathbb{P 3$), and is mainly interesting for irregular surfaces, since in the regular case a similar but simpler result (due to Catanese) was already known. The theorem essentially states that giving a good birational weighted canonical projection is equivalent to giving a symmetric morphism of (graded) vector bundles on $\overline{\mathbb{P ({\rm w )$, satisfying some suitable conditions. Such a morphism is then explicitly determined in chapter 4 for a family of surfaces with numerical invariant