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- Title
On the First Hochschild Cohomology of Cocommutative Hopf Algebras of Finite Representation Type.
- Authors
Chang, Hao
- Abstract
Let |$\mathscr{B}_0({\mathcal{G}})\subseteq k\,{\mathcal{G}}$| be the principal block algebra of the group algebra |$k\,{\mathcal{G}}$| of an infinitesimal group scheme |${\mathcal{G}}$| over an algebraically closed field |$k$| of characteristic |${\operatorname{char}}(k)=:p\geq 3$|. We calculate the restricted Lie algebra structure of the first Hochschild cohomology |${\mathcal{L}}:={\operatorname{H}}^1(\mathscr{B}_0({\mathcal{G}}),\mathscr{B}_0({\mathcal{G}}))$| whenever |$\mathscr{B}_0({\mathcal{G}})$| has finite representation type. As a consequence, we prove that the complexity of the trivial |${\mathcal{G}}$| -module |$k$| coincides with the maximal toral rank of |${\mathcal{L}}$|.
- Subjects
HOPF algebras; LIE algebras; REPRESENTATIONS of algebras; COHOMOLOGY theory; GROUP algebras
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 3, p1131
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa020