Exactness of complexes of modules over schur superalgebras

Alexandr N. Grishkov; František Marko; Alexandr N. Zubkov

doi:10.1142/S1005386706000125

Exactness of complexes of modules over schur superalgebras

Alexandr N. Grishkov, František Marko, Alexandr N. Zubkov

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study tensor products of injective modules and exactness of certain naturally appearing complexes of projective and injective modules over Schur superalgebras over an algebraically closed field K of characteristic p > 2. In particular, for the complex 0 → P(0) →^u0 P(1) →^u1 ⋯ →^ur-2 P(r-1) →^ur-1 P(r) → 0 of projective modules P(i) = Sξ_1i(m+1)^r-1 given by multiplication by u_i = ξ_1i(m+1) ^r-i, 1ⁱ⁺¹(m+1)^r-i-1, we determine all of the terms where it is exact.

Original language	English
Pages (from-to)	99-110
Number of pages	12
Journal	Algebra Colloquium
Volume	13
Issue number	1
DOIs	https://doi.org/10.1142/S1005386706000125
Publication status	Published - Mar 2006
Externally published	Yes

Keywords

Complexes
Representations of finite-dimensional algebras
Schur superalgebras

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1142/S1005386706000125

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year = "2006",

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T1 - Exactness of complexes of modules over schur superalgebras

AU - Grishkov, Alexandr N.

AU - Marko, František

AU - Zubkov, Alexandr N.

PY - 2006/3

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N2 - In this paper, we study tensor products of injective modules and exactness of certain naturally appearing complexes of projective and injective modules over Schur superalgebras over an algebraically closed field K of characteristic p > 2. In particular, for the complex 0 → P(0) →u0 P(1) →u1 ⋯ →ur-2 P(r-1) →ur-1 P(r) → 0 of projective modules P(i) = Sξ1i(m+1)r-1 given by multiplication by ui = ξ1i(m+1) r-i, 1i+1(m+1)r-i-1, we determine all of the terms where it is exact.

AB - In this paper, we study tensor products of injective modules and exactness of certain naturally appearing complexes of projective and injective modules over Schur superalgebras over an algebraically closed field K of characteristic p > 2. In particular, for the complex 0 → P(0) →u0 P(1) →u1 ⋯ →ur-2 P(r-1) →ur-1 P(r) → 0 of projective modules P(i) = Sξ1i(m+1)r-1 given by multiplication by ui = ξ1i(m+1) r-i, 1i+1(m+1)r-i-1, we determine all of the terms where it is exact.

KW - Complexes

KW - Representations of finite-dimensional algebras

KW - Schur superalgebras

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Exactness of complexes of modules over schur superalgebras

Abstract

Keywords

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