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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics