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17a70 (primary)

Bulletin of the London Mathematical Society (1)

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SCHUR SUPERALGEBRAS IN CHARACTERISTIC p, II
FRANTIšEK MARKO, ALEXANDR N. ZUBKOV
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 1 / February 2006

Published online by Cambridge University Press:

30 January 2006, pp. 99-112

Print publication:

February 2006
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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 $r$.