Lectures in Algebraic Combinatorics: Young`s Construction, Seminormal Representations, Sl(2) Representations, Heaps, Basics on Finite Fields, Garsia Adriano M., Eğecioğlu Цmer

Автор: Walker, Grant (university Of Manchester) Wood, Reginald M. W. (university Of Manchester)
Название: Polynomials and the mod 2 steenrod algebra: volume 2, representations of gl (n,f2)
ISBN: 1108414451 ISBN-13(EAN): 9781108414456
Издательство: Cambridge Academ
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Цена: 81300.00 T
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Описание: This detailed two-volume reference on the Steenrod algebra and its various applications presents more than thirty years of research. This second volume broadens the discussion to include modular representations of matrix groups.

Автор: Ion Colojoara, Aurelian Gheondea
Название: Lectures on Representations of Locally Compact Groups
ISBN: 6068443108 ISBN-13(EAN): 9786068443102
Издательство: Mare Nostrum (Eurospan)
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Описание: This is a modern presentation of the theory of representations of locally compact groups. In a small number of pages, the reader can get some of the most important theorems on this subject. Many examples are provided.Highlights of the volume include:(1) A generous introduction explaining the origins of group theory and their representations, the motivation for the main problems in this theory, and the deep connections with modern physics.(2) A solid presentation of the theory of topological groups and of Lie groups.(3) Two proofs of the existence of Haar measures.(4) The detailed study of continuous representations on general locally convex spaces, with an emphasis on unitary representations of compact groups on Hilbert spaces.(5) A careful presentation of induced representations on locally convex spaces and G. W. Mackey's Theorem of Imprimitivity.About half of the results included in this volume appear for the first time in a book, while the theory of $p$-induced representations on locally convex spaces is new. To facilitate reading, several appendices present the concepts and basic results from general topology, differential manifolds, abstract measures and integration, topological vector spaces, Banach spaces, Banach algebras, $C^*$-algebras, and operator theory on Hilbert spaces.

Автор: Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff
Название: Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
ISBN: 1470451743 ISBN-13(EAN): 9781470451745
Издательство: Mare Nostrum (Eurospan)
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Описание: A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.