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Extensions of tame algebras and finite group schemes of domestic representation type
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Rolf Farnsteiner
Published/Copyright:
March 14, 2013
Abstract
Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k-algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These results are then used to show that principal blocks of finite group schemes of odd characteristic are of polynomial growth if and only if they are Morita equivalent to trivial extensions of radical square zero tame hereditary algebras. In that case, the blocks are of domestic representation type and the underlying group schemes are closely related to binary polyhedral group schemes.
Keywords: Group schemes; domestic representation type
Funding source: DFG
Award Identifier / Grant number: priority program SPP1388 `Darstellungstheorie'
Received: 2012-8-8
Revised: 2012-12-16
Published Online: 2013-3-14
Published in Print: 2015-3-1
© 2015 by De Gruyter
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- Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
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Articles in the same Issue
- Frontmatter
- Near abelian profinite groups
- On Calabi–Yau threefolds associated to a web of quadrics
- On the partial fraction decomposition of the restricted partition generating function
- Projectively flat Finsler manifolds with infinite dimensional holonomy
- Weighted version of Carleson measure and multilinear Fourier multiplier
- Injective objects and retracts of Fraïssé limits
- On hypersurfaces containing projective varieties
- Additive reducts of algebraically closed valued fields
- On the subconvexity problem for GL(3) × GL(2) L-functions
- An algebraic property of Hecke operators and two indefinite theta series
- Sum formula of multiple Hurwitz-zeta values
- Classification of homogeneous holomorphic hermitian principal bundles over G/K
- Integrality properties of the CM-values of certain weak Maass forms
- Heat kernel for fractional diffusion operators with perturbations
- New class of multiple weights and new weighted inequalities for multilinear operators
- Balanced Hermitian geometry on 6-dimensional nilmanifolds
- Extensions of tame algebras and finite group schemes of domestic representation type
- Weighted estimates for multilinear Fourier multipliers
- Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
- From ring epimorphisms to universal localisations
- Brauer algebras of type B
- Existence problems for the p-Laplacian
- Averaging operators over nondegenerate quadratic surfaces in finite fields
- Lawson homology for abelian varieties
