On regular subalgebras of a symmetrizable Kac-Moody algebra
نویسندگان
چکیده
منابع مشابه
Regular Subalgebras of Affine Kac–moody Algebras
We classify regular subalgebras of affine Kac–Moody algebras in terms of their root systems. In the process, we establish that a root system of a subalgebra is always an intersection of the root system of the algebra with a sublattice of its root lattice. We also discuss applications to investigations of regular subalgebras of hyperbolic Kac–Moody algebras and conformally invariant subalgebras ...
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Kirillov-Reshetikhin and Levendorskii-Soibelman developed a formula for the universal R-matrix of Uq(g) of the form R = (X ⊗X)∆(X). The action of X on a representation V permutes weight spaces according to the longest element in the Weyl group, so is only defined when g is of finite type. We give a similar formula which is valid for any symmetrizable KacMoody algebra. This is done by replacing ...
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Let Gm resp. Gf be the minimal resp. formal Kac-Moody group, associated to a symmetrizable generalized Cartan matrix, over a field F of characteristic 0. Let F [Gm] be the algebra of strongly regular functions on Gm. We denote by Ĝm resp. Ĝf certain monoid completions of Gm resp. Gf , build by using the faces of the Tits cone. We show that there is an action of Ĝf × Ĝf on the spectrum of F-valu...
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In this paper we utilize the notion of infinite dimensional diffeological Lie groups and diffeological Lie algebras to construct a Lie group structure on the space of smooth paths into a completion of a generalized Kac-Moody Lie algebra associated to a symmetrized generalized Cartan matrix. We then identify a large normal subgroup of this group of paths such that the quotient group has the soug...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1991
ISSN: 0386-2194
DOI: 10.3792/pjaa.67.117