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Invariants of coinvariant algebras

  • Larry Smith
Published/Copyright: May 29, 2014
Forum Mathematicum
From the journal Forum Mathematicum Volume 27 Issue 6

Abstract

Let ρ:G↪ GL (n,𝔽) be a representation of a finite group G over the field 𝔽 and let H≤G be a subgroup of G. Form the algebra of polynomial functions 𝔽[V] on the representation space V=𝔽n of ρ. The action of G on V extends to 𝔽[V] and we denote by 𝔽[V]G the invariant algebra; namely, the subalgebra of G-invariant forms. The coinvariant algebra of ρ is the quotient algebra 𝔽[V]G=𝔽[V]/𝔥(G) where the Hilbert ideal𝔥(G) of G (or better put, of ρ) is the ideal of 𝔽[V] generated by all the homogeneous G-invariant forms of strictly positive degree. The group H acts on 𝔽[V]G and the subject of this manuscript is the algebra (𝔽[V]G)H of H-invariants of 𝔽[V]G.

Keywords: Invariant theory; Poincaré duality algebras
MSC: 13A50; 13B02; 13E10; 13H05
Received: 2013-9-17
Revised: 2014-3-17
Published Online: 2014-5-29
Published in Print: 2015-11-1

© 2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Conjugacy classes of finite groups and graph regularity
  3. A note about complexity of lens spaces
  4. A note for alternating Ramanujan's circular summation formula
  5. On a question of Gillespie
  6. Jumping pairs of Steiner bundles
  7. On the recurrence of symmetric jump processes
  8. R-groups, elliptic representations, and parameters for GSpin groups
  9. The least common multiple of consecutive quadratic progression terms
  10. Hybrid bounds for quadratic Weyl sums and arithmetic applications
  11. Invariants of coinvariant algebras
  12. Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces
  13. Distinction of the Steinberg representation II: An equality of characters
  14. Perturbations of functional inequalities for Lévy type Dirichlet forms
  15. Decomposable Leavitt path algebras for arbitrary graphs
  16. Group rings whose set of symmetric elements is Lie metabelian
  17. Heat kernel and Lipschitz–Besov spaces
  18. A case of monoidal uniqueness of algebraic models
  19. Schur tensor product of operator spaces
  20. On the upper bound for Bi(K)Bi(K*)
  21. Bredon cohomological dimensions for proper actions and Mackey functors
  22. Action of the Cremona group on foliations on ℙℂ2: Some curious facts
  23. Homological aspects of the dual Auslander transpose
  24. Nilpotent covers and non-nilpotent subsets of finite groups of Lie type
  25. Erratum to The distribution of the logarithm in an orthogonal and a symplectic family of L-functions [Forum Math. 26 (2014), 523–546]
https://doi.org/10.1515/forum-2013-0151
Keywords for this article
Invariant theory; Poincaré duality algebras

Articles in the same Issue

  1. Frontmatter
  2. Conjugacy classes of finite groups and graph regularity
  3. A note about complexity of lens spaces
  4. A note for alternating Ramanujan's circular summation formula
  5. On a question of Gillespie
  6. Jumping pairs of Steiner bundles
  7. On the recurrence of symmetric jump processes
  8. R-groups, elliptic representations, and parameters for GSpin groups
  9. The least common multiple of consecutive quadratic progression terms
  10. Hybrid bounds for quadratic Weyl sums and arithmetic applications
  11. Invariants of coinvariant algebras
  12. Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces
  13. Distinction of the Steinberg representation II: An equality of characters
  14. Perturbations of functional inequalities for Lévy type Dirichlet forms
  15. Decomposable Leavitt path algebras for arbitrary graphs
  16. Group rings whose set of symmetric elements is Lie metabelian
  17. Heat kernel and Lipschitz–Besov spaces
  18. A case of monoidal uniqueness of algebraic models
  19. Schur tensor product of operator spaces
  20. On the upper bound for Bi(K)Bi(K*)
  21. Bredon cohomological dimensions for proper actions and Mackey functors
  22. Action of the Cremona group on foliations on ℙℂ2: Some curious facts
  23. Homological aspects of the dual Auslander transpose
  24. Nilpotent covers and non-nilpotent subsets of finite groups of Lie type
  25. Erratum to The distribution of the logarithm in an orthogonal and a symplectic family of L-functions [Forum Math. 26 (2014), 523–546]
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