Cross-projective representations of pairs of anticommutative algebras, alloys and finite-dimensional irreducible representations of some infinite-dimensional Lie algebras

Details Cross-projective representations of pairs of anticommutative algebras, alloys and finite-dimensional irreducible representations of some infinite-dimensional Lie algebras Cross-projective representations of pairs of anticommutative algebras, alloys and finite-dimensional irreducible representations of some infinite-dimensional Lie algebras

1998-06-02

arxiv.org/abs/math/9806005v1

Mathematics

Representation Theory

AMSTEX

Scientific paper

The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their representations, quaternary algebras and their alloyability are discussed. Considered examples allow to conclude that new representations have some intriguing features (continuous moduli of finite-dimensional irreducible representations, sophisticated Clebsch-Gordan coefficient calculus, etc.).

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