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Start Over Topic algebra Topic loop algebra Topic mathematics Journal transactions of the american mathematical society
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1. Drinfeld-type presentations of loop algebras.

Author

Chen, Fulin, Jing, Naihuan, Kong, Fei, and Tan, Shaobin

Subjects
KAC-Moody algebras, UNIVERSAL algebra, ALGEBRA, LIE algebras, LOOPS (Group theory), MATHEMATICS
Abstract

Let g be the derived subalgebra of a Kac-Moody Lie algebra of finite-type or affine-type, let μ be a diagram automorphism of g, and let L(g,μ) be the loop algebra of g associated to μ. In this paper, by using the vertex algebra technique, we provide a general construction of current-type presentations for the universal central extension g[μ] of L(g,μ). The construction contains the classical limit of Drinfeld's new realization for (twisted and untwisted) quantum affine algebras [Soviet Math. Dokl. 36 (1988), pp. 212-216] and the Moody-Rao-Yokonuma presentation for toroidal Lie algebras [Geom. Dedicata 35 (1990), pp. 283-307] as special examples. As an application, when g is of simply-laced-type, we prove that the classical limit of the μ-twisted quantum affinization of the quantum Kac-Moody algebra associated to g introduced in [J. Math. Phys. 59 (2018), 081701] is the universal enveloping algebra of g[μ]. [ABSTRACT FROM AUTHOR]

Published
2020
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2. Orthogonal symmetric affine Kac-Moody algebras

Author

Walter Freyn

Subjects
Symmetric algebra, Pure mathematics, Quantum affine algebra, Jordan algebra, Loop algebra, Applied Mathematics, General Mathematics, Clifford algebra, Kac–Moody algebra, Affine Lie algebra, Algebra, High Energy Physics::Theory, Mathematics::Quantum Algebra, Mathematics::Representation Theory, Generalized Kac–Moody algebra, Mathematics
Abstract

Riemannian symmetric spaces are fundamental objects in finite dimensional differential geometry. An important problem is the construction of symmetric spaces for generalizations of simple Lie groups, especially their closest infinite dimensional analogues, known as affine Kac-Moody groups. We solve this problem and construct affine Kac-Moody symmetric spaces in a series of several papers. This paper focuses on the algebraic side; more precisely, we introduce OSAKAs, the algebraic structures used to describe the connection between affine Kac-Moody symmetric spaces and affine Kac-Moody algebras and describe their classification.

Published
2015