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Author: Seok-Jin Kang
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Author: Seok-Jin Kang
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
 PDF](https://books.google.com/books/content/images/frontcover/R6xTAQAACAAJ?fife=w80-h100)
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Languages : en
Pages :
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Victor Kac and Robert Moody independently introduced Kac-Moody algebras around 1968. These Lie algebras have numerous applications in physics and mathematics and thus have been the subject of much study over the last three decades. Kac-Moody algebras are classified as finite, affine, or indefinite type. A basic problem concerning these algebras is finding their root multiplicities. The root multiplicities of finite and affine type Kac-Moody algebras are well known. However, determining the root multiplicities of indefinite type Kac-Moody algebras is an open problem. In this thesis we determine the multiplicities of some roots of the indefinite type Kac-Moody algebras HC[subscript n](1). A well known construction allows us to view HC[subscript n](1) as the minimal graded Lie algebra with local part V direct sum g0 direct sum V', where g0 is the affine Kac-Moody algebra C[subscript n](1). and V, V' are suitable g0-modules. From this viewpoint, root spaces of HC[subscript n](1) become weight spaces of certain C[subscript n](1)-modules. Using a multiplicity formula due to Kang we reduce our problem to finding weight multiplicities in certain irreducible highest weight C[subscript n](1)-modules. We then use crystal basis theory for the affine Kac-Moody algebras C[subscript n](1) to find these weight multiplicities. With this strategy we calculate the multiplicities of some roots of HC[subscript n](1). In particular, we determine the multiplicities of the level two roots -2(alpha1)-k(delta) of HC[subscript n](1) for 1 less than or equal to k less than or equal to 10. We also show that the multiplicities of the roots of HC[subscript n](1) of the form -l(alpha−1) -k(delta) are n for l equal to k and 0 for l greater than k. In the process, we observe that Frenkel's c.
Author: Peter Niemann
Publisher: American Mathematical Soc.
ISBN: 0821828886
Category : Mathematics
Languages : en
Pages : 137
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Book Description
Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.
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Author: Mathematical Sciences Research Institute (Berkeley, Calif.).
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Category :
Languages : en
Pages :
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Author: Neelacanta Sthanumoorthy
Publisher: American Mathematical Soc.
ISBN: 0821833375
Category : Mathematics
Languages : en
Pages : 384
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Book Description
This volume is the proceedings of the Ramanujan International Symposium on Kac-Moody Lie algebras and their applications. The symposium provided researchers in mathematics and physics with the opportunity to discuss new developments in this rapidly-growing area of research. The book contains several excellent articles with new and significant results. It is suitable for graduate students and researchers working in Kac-Moody Lie algebras, their applications, and related areas of research.
Author: Vicky Lynn Williams
Publisher:
ISBN:
Category :
Languages : en
Pages : 122
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Book Description
Keywords: root multiplicities, representation theory, Kac-Moody algebras, Lie algebras.
Author: Evan Andrew Wilson
Publisher:
ISBN:
Category :
Languages : en
Pages : 73
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Author: Sarah Kathryn Spencer
Publisher:
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Category : Kac-Moody algebras
Languages : en
Pages : 29
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Author: Mathematical Sciences Research Institute (Berkeley, Calif.).
Publisher:
ISBN:
Category :
Languages : en
Pages : 41
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Author: Neelacanta Sthanumoorthy
Publisher: Academic Press
ISBN: 012804683X
Category : Mathematics
Languages : en
Pages : 514
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Book Description
Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. - Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory - Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities - Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras - Focuses on Kac-Moody algebras
