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Maximal subalgebras of finite-dimensional algebras

  • Miodrag Cristian Iovanov und Alexander Harris Sistko EMAIL logo
Veröffentlicht/Copyright: 14. Juni 2019
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 31 Heft 5

Abstract

We study maximal associative subalgebras of an arbitrary finite-dimensional associative algebra B over a field 𝕂 and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case and then lifting to non-semisimple algebras. The results are sharpest in the case of algebraically closed fields and take special forms for algebras presented by quivers with relations. We also relate representation theoretic properties of the algebra and its maximal and other subalgebras and provide a series of embeddings between quivers, incidence algebras and other structures which relate indecomposable representations of algebras and some subalgebras via induction/restriction functors. Some results in literature are also re-derived as a particular case, and other applications are given.

Keywords: Maximal subalgebra; semisimple algebra; separable functor; separable; split; split-by-nilpotent
MSC 2010: 16S99; 16G60; 16G10; 16S50; 16W20

Communicated by Freydoon Shahidi

Acknowledgements

The authors would like to thank Ryan Kinser for a careful reading of a preliminary version of this paper and many useful suggestions which improved the paper; they would also like to thank Victor Camillo for encouraging discussions and suggesting a few additional references.

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Received: 2019-02-05
Published Online: 2019-06-14
Published in Print: 2019-09-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Selberg integral over local fields
  3. On conjugation orbits of semisimple pairs in rank one
  4. On a topology property for the moduli space of Kapustin–Witten equations
  5. Differentiability of the evolution map and Mackey continuity
  6. A prime geodesic theorem for SL3(ℤ)
  7. Comparison and continuity of Wick-type star products on certain coadjoint orbits
  8. A construction of residues of Eisenstein series and related square-integrable classes in the cohomology of arithmetic groups of low k-rank
  9. Linear invariance of intersections on unitary Rapoport–Zink spaces
  10. Maximal subalgebras of finite-dimensional algebras
  11. A universal enveloping algebra for cocommutative rack bialgebras
  12. A rank rigidity result for CAT(0) spaces with one-dimensional Tits boundaries
  13. Projective objects in the category of pointwise finite dimensional representations of an interval finite quiver
https://doi.org/10.1515/forum-2019-0033
Schlagwörter für diesen Artikel
Maximal subalgebra; semisimple algebra; separable functor; separable; split; split-by-nilpotent

Artikel in diesem Heft

  1. Frontmatter
  2. Selberg integral over local fields
  3. On conjugation orbits of semisimple pairs in rank one
  4. On a topology property for the moduli space of Kapustin–Witten equations
  5. Differentiability of the evolution map and Mackey continuity
  6. A prime geodesic theorem for SL3(ℤ)
  7. Comparison and continuity of Wick-type star products on certain coadjoint orbits
  8. A construction of residues of Eisenstein series and related square-integrable classes in the cohomology of arithmetic groups of low k-rank
  9. Linear invariance of intersections on unitary Rapoport–Zink spaces
  10. Maximal subalgebras of finite-dimensional algebras
  11. A universal enveloping algebra for cocommutative rack bialgebras
  12. A rank rigidity result for CAT(0) spaces with one-dimensional Tits boundaries
  13. Projective objects in the category of pointwise finite dimensional representations of an interval finite quiver
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