Seaweeds Arising from Brauer Configuration Algebras

Agustín Moreno Cañadas () and Odette M. Mendez
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Agustín Moreno Cañadas: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
Odette M. Mendez: Departamento de Matemáticas, Universidad Nacional de Colombia, Campus La Nubia, Manizales 170003, Colombia

Mathematics, 2023, vol. 11, issue 8, 1-18

Abstract: Seaweeds or seaweed Lie algebras are subalgebras of the full-matrix algebra Mat ( n ) introduced by Dergachev and Kirillov to give an example of algebras for which it is possible to compute the Dixmier index via combinatorial methods. It is worth noting that finding such an index for general Lie algebras is a cumbersome problem. On the other hand, Brauer configuration algebras are multiserial and symmetric algebras whose representation theory can be described using combinatorial data. It is worth pointing out that the set of integer partitions and compositions of a fixed positive integer give rise to Brauer configuration algebras. However, giving a closed formula for the dimension of these kinds of algebras or their centers for all positive integer is also a tricky problem. This paper gives formulas for the dimension of Brauer configuration algebras (and their centers) induced by some restricted compositions. It is also proven that some of these algebras allow defining seaweeds of Dixmier index one.

Keywords: Brauer configuration algebra; integer partition; quiver representation; seaweed algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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