TY - JOUR
T1 - Schur superalgebras in characteristic p
AU - Marko, František
AU - Zubkov, Alexandr N.
N1 - Funding Information:
This research was done during the second author’s visit to São Paulo University, Brazil, sponsored by FAPESP. The second author thanks Alexandr Grishkov whose efforts played crucial role to make this visit possible. The second author also thanks for support from RFFI (grant N 01-01-00674) and especially Stephen Donkin for valuable help. We are grateful for all of this support.
PY - 2006/2
Y1 - 2006/2
N2 - The structure of a Schur superalgebra S = 5(1 | 1, r) in odd characteristic p is completely determined. The algebra S is semisimple if and only if p does not divide r. If p divides r, then simple S-modules are one-dimensional and the quiver and relations of S can be immediately seen from its regular representation computed in this paper. Surprisingly, if p divides r, then S is neither quasi-hereditary nor cellular nor stratified, as one would expect by analogy with classical Schur algebras or Schur superalgebras in characteristc zero.
AB - The structure of a Schur superalgebra S = 5(1 | 1, r) in odd characteristic p is completely determined. The algebra S is semisimple if and only if p does not divide r. If p divides r, then simple S-modules are one-dimensional and the quiver and relations of S can be immediately seen from its regular representation computed in this paper. Surprisingly, if p divides r, then S is neither quasi-hereditary nor cellular nor stratified, as one would expect by analogy with classical Schur algebras or Schur superalgebras in characteristc zero.
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U2 - 10.1007/s10468-005-9001-2
DO - 10.1007/s10468-005-9001-2
M3 - Article
AN - SCOPUS:33646721146
SN - 1386-923X
VL - 9
SP - 1
EP - 12
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 1
ER -