# Combinatorics Seminar 2015

Date: Sat, May 09, 2015

Time: 09:15 - 10:00

Venue: Middle Meeting Room

Title: Primary modules for the tetrahedron algebra

Abstract:

Our talk is about a certain Lie algebra called the tetrahedron algebra, or 'tet' for short, and denoted by $\boxtimes$. The tet algebra is defined by generators and relations. A $\boxtimes$-module $V$ is called primary whenever $V$ has positive dimension and the square of each $\boxtimes$-generator is the identity on $V$. Our main results include (i) the classification up to isomorphism of the primary $\boxtimes$-modules; (ii) a description of the submodules for a primary $\boxtimes$-module; (iii) necessary and sufficient conditions for a primary $\boxtimes$-module to be a direct sum of irreducible submodules.

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