Izvorni znanstveni članak

https://doi.org/10.21857/y6zolb4v6m

On bases of g-invariant endomorphism algebras

Jing-Song Huang orcid.org/0000-0001-6910-0606 ; Mathematics Research Center, School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China
Yufeng Zhao ; Department of Mathematics, Peking University, Beijing, China

Sažetak

Let g be a complex simple Lie algebra. Let Z(g) be the center of the universal enveloping algebra U(g). Let Vλ be the finite-dimensional irreducible g-module with highest weight λ. Our main result is a criterion of the existence of Z(g)-bases for the g-invariant endomorphism algebra Rλ=: Homg(End Vλ,U(g)). Then we obtain a Clifford algebra analogue, namely a criterion of the existence C(g)g-bases for RλC =: Homg(End Vλ,C(g)). We also describe a criterion of the existence of bases generated by powers of the Casimir element for R{λ,ν} =: Homg(End Vλ, End Vν).

Ključne riječi

Simple Lie algebra; Casimir operator; invariant endomorphism algebra

Hrčak ID:

313637

URI

https://hrcak.srce.hr/313637

Datum izdavanja:

24.1.2024.

Posjeta: 601 *