Let F be a field of characteristic zero and let A be an Falgebra graded by a finite group G of order k . Given a non-negative integer n and a sum n = n1 1 + + nk k of k non-negative integers, we associate a S ( n )-module to A , where S ( n ) := S n 1 x x Snk, n k , and we denote its S ( n )-character by chi ( n ) ( A ). In this paper, for all sum n = n1 1 + +nk, n k , we make explicit the decomposition of chi ( n ) ( A ) for some important G-graded algebras A and we compute the number lG n(A) G n ( A ) of irreducibles appearing in all such decompositions. Our main goal is to classify G-graded algebras A such that the sequence lGn(A) G n ( A ) is bounded by three.
Cota, W.Q., Ioppolo, A., Martino, F., Vieira, A.C. (2024). On the colength sequence of G-graded algebras. LINEAR ALGEBRA AND ITS APPLICATIONS, 701, 61-96 [10.1016/j.laa.2024.08.005].
On the colength sequence of G-graded algebras
Ioppolo, AntonioSecondo
;Martino, FabrizioPenultimo
;
2024-01-01
Abstract
Let F be a field of characteristic zero and let A be an Falgebra graded by a finite group G of order k . Given a non-negative integer n and a sum n = n1 1 + + nk k of k non-negative integers, we associate a S ( n )-module to A , where S ( n ) := S n 1 x x Snk, n k , and we denote its S ( n )-character by chi ( n ) ( A ). In this paper, for all sum n = n1 1 + +nk, n k , we make explicit the decomposition of chi ( n ) ( A ) for some important G-graded algebras A and we compute the number lG n(A) G n ( A ) of irreducibles appearing in all such decompositions. Our main goal is to classify G-graded algebras A such that the sequence lGn(A) G n ( A ) is bounded by three.File | Dimensione | Formato | |
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Graded_colengths.pdf
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On the colength sequence of G-graded algebras.pdf
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