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SCHUR SUPERALGEBRAS IN CHARACTERISTIC p, II

Published online by Cambridge University Press:  30 January 2006

FRANTIšEK MARKO  and
ALEXANDR N. ZUBKOV
FRANTIšEK MARKO
Affiliation:
Pennsylvania State University, 76 University Drive, Hazleton, PA 18202, USAfxm13@psu.edu
ALEXANDR N. ZUBKOV
Affiliation:
Omsk State Pedagogical University, Chair of Geometry, 644099 Omsk-99, Tuhachevskogo Embankment 14, Russiazubkov@iitam.omsk.net.ru
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Abstract

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 $m,n \ge 1$ 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 $r$.

Keywords

17A70 (primary)20C30 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 1 , February 2006 , pp. 99 - 112
Copyright
The London Mathematical Society 2006

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