Quiver concomitants are often reflexive Azumaya
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- by Lieven Le Bruyn PDF
- Proc. Amer. Math. Soc. 105 (1989), 10-16 Request permission
Abstract:
In this note we show that the concomitants of a quiver with symmetric Ringel form associated to a root from the fundamental chamber is a reflexive Azumaya algebra except for low dimensional anomalities.References
- M. Artin, On Azumaya algebras and finite dimensional representations of rings, J. Algebra 11 (1969), 532–563. MR 242890, DOI 10.1016/0021-8693(69)90091-X
- V. G. Kac, Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), no. 1, 57–92. MR 557581, DOI 10.1007/BF01403155
- Lieven Le Bruyn, A cohomological interpretation of the reflexive Brauer group, J. Algebra 105 (1987), no. 1, 250–254. MR 871757, DOI 10.1016/0021-8693(87)90190-6
- Lieven Le Bruyn, The Artin-Schofield theorem and some applications, Comm. Algebra 14 (1986), no. 8, 1439–1455. MR 859443, DOI 10.1080/00927878608823375
- Lieven Le Bruyn and Claudio Procesi, Semisimple representations of quivers, Trans. Amer. Math. Soc. 317 (1990), no. 2, 585–598. MR 958897, DOI 10.1090/S0002-9947-1990-0958897-0 —, Etale local structure of matrixinvariants and concomitants (Proc. Algebraic Groups Utrecht, 1986), Lecture Notes in Math., vol. 1271, Springer-Verlag 1987, pp. 143-176.
- Shuen Yuan, Reflexive modules and algebra class groups over noetherian integrally closed domains, J. Algebra 32 (1974), 405–417. MR 357463, DOI 10.1016/0021-8693(74)90149-5
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 10-16
- MSC: Primary 16A46; Secondary 13A20, 14M20, 16A64, 20G15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0931734-3
- MathSciNet review: 931734