منابع مشابه
Lie Group Representations on Polynomial Rings
0. Introduction. 1. Let G be a group of linear transformations on a finite dimensional real or complex vector space X. Assume X is completely reducible as a G-module. Let 5 be the ring of all complexvalued polynomials on X, regarded as a G-module in the obvious way, and let J C 5 be the subring of all G-invariant polynomials on X. Now let J be the set of all ƒ £ J having zero constant term and ...
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The classification of 2-step nilpotent Lie algebras is attacked by a generator-relation method. The main results are in low dimensions or a small number of relations. Introduction. According to a theorem of Levi, in characteristic zero a finitedimensional Lie algebra can be written as the direct sum of a semisimple subalgebra and its unique maximal solvable ideal. If the field is algebraically ...
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We study free centre-by-metabelian Lie algebras over a field of characteristic 2. By using homological methods, we determine the dimensions of the fine homogeneous components of the second-derived algebra. In conjunction with earlier results by Mansuroǧlu and the second author, this leads to a complete description of the additive structure of the second-derived ideal in the free centre-by-metab...
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Given a Lie superalgebra g, we introduce several variants of the representation ring, built as subrings and quotients of the ring RZ2(g) of virtual g-supermodules, up to (even) isomorphisms. In particular, we consider the ideal R+(g) of virtual g-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring SR(g) on which the parity rever...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1992
ISSN: 0021-8693
DOI: 10.1016/0021-8693(92)90123-4