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Schur Superalgebras in Characteristic p , II
Author(s) -
Marko František,
Zubkov Alexandr N.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305018187
Subject(s) - mathematics , corollary , mathematics subject classification , superalgebra , dimension (graph theory) , pure mathematics , field (mathematics) , zero (linguistics) , lie superalgebra , algebra over a field , linguistics , current algebra , philosophy , affine lie algebra
It is proved that if a Schur superalgebra is not semisimple, then it is neither cellular nor quasi‐hereditary (Theorem 2), and it has infinite global dimension (Corollary 18). The algebra S ( m | n, r ) with m, n ⩾ 1 is semisimple if and only if p , the characteristic of the ground field, is zero or greater than r , or when m = n = 1 and p does not divide r . 2000 Mathematics Subject Classification 17A70 (primary), 20C30 (secondary).