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Star-group identities on units of group algebras: The non-torsion case

  • Antonio Giambruno ORCID logo EMAIL logo , Cesar Polcino Milies und Sudarshan K. Sehgal
Veröffentlicht/Copyright: 17. Juni 2017
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 30 Heft 1

Abstract

Let G be a group, F a field and FG the corresponding group algebra. We consider an involution on FG which is the linear extension of an involution of G, e.g., g*=g-1 for g∈G. This paper is focused on the characterization of a non-torsion group G provided the group of units U⁢(F⁢G) satisfies a *-group identity. The torsion case was studied in [7], and when * is the classical involution, this problem was solved in the case of symmetric units in [21].

Keywords: Group algebra; involution; unit; group identity
MSC 2010: 16U60; 16W10

Communicated by Manfred Droste

Funding statement: The first author was partially supported by GNSAGA of INDAM. The second author was partially supported by CNPq., Proc. 300243/79-0(RN) and FAPESP, Proc 2009/52665-0. The third author was supported by NSERC

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Received: 2016-12-27
Revised: 2017-05-03
Published Online: 2017-06-17
Published in Print: 2018-01-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Logarithmic Sobolev inequalities for Moebius measures on spheres
  3. Delta sets for nonsymmetric numerical semigroups with embedding dimension three
  4. Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L2(ℝ+;dx/x)
  5. Remarks on Lp-limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems
  6. On blocks with one modular character
  7. On the large-scale geometry of diffeomorphism groups of 1-manifolds
  8. Lp boundedness of rough bi-parameter Fourier integral operators
  9. Coclosed G2-structures inducing nilsolitons
  10. Existence of solutions for a semirelativistic Hartree equation with unbounded potentials
  11. On two questions concerning representations distinguished by the Galois involution
  12. Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains
  13. Nevanlinna-type theorems for meromorphic functions on non-positively curved Kähler manifolds
  14. The splitting of cohomology of p-groups with rank 2
  15. Star-group identities on units of group algebras: The non-torsion case
  16. Expansion for cubes in the Heisenberg group
  17. Semilinear Robin problems resonant at both zero and infinity
  18. Purely infinite simple Kumjian–Pask algebras
https://doi.org/10.1515/forum-2016-0266
Schlagwörter für diesen Artikel
Group algebra; involution; unit; group identity

Artikel in diesem Heft

  1. Frontmatter
  2. Logarithmic Sobolev inequalities for Moebius measures on spheres
  3. Delta sets for nonsymmetric numerical semigroups with embedding dimension three
  4. Two versions of pseudo-differential operators involving the Kontorovich–Lebedev transform in L2(ℝ+;dx/x)
  5. Remarks on Lp-limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems
  6. On blocks with one modular character
  7. On the large-scale geometry of diffeomorphism groups of 1-manifolds
  8. Lp boundedness of rough bi-parameter Fourier integral operators
  9. Coclosed G2-structures inducing nilsolitons
  10. Existence of solutions for a semirelativistic Hartree equation with unbounded potentials
  11. On two questions concerning representations distinguished by the Galois involution
  12. Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains
  13. Nevanlinna-type theorems for meromorphic functions on non-positively curved Kähler manifolds
  14. The splitting of cohomology of p-groups with rank 2
  15. Star-group identities on units of group algebras: The non-torsion case
  16. Expansion for cubes in the Heisenberg group
  17. Semilinear Robin problems resonant at both zero and infinity
  18. Purely infinite simple Kumjian–Pask algebras
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