Quiver concomitants are often reflexive Azumaya

Author:
Lieven Le Bruyn

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[Ar]**M. Artin,*On Azumaya algebras and finite dimensional representations of rings*, J. Algebra**11**(1969), 532-563. MR**0242890 (39:4217)****[Ka]**V. Kac,*Infinite root systems, representations of graphs and invariant theory*, Invent. Math.**56**(1980), 57-92. MR**557581 (82j:16050)****[L]**L. Le Bruyn,*A cohomological interpretation of the reflexive Brauer group*, J. Algebra**105**(1987), 250-254. MR**871757 (88j:16009)****[L2]**-,*The Artin-Schofield theorem and some consequences*, Comm. Algebra**14**(8) (1986), 1439-1455. MR**859443 (87k:16020)****[LP]**L. Le Bruyn and C. Procesi,*Semisimple representations of quivers*, Trans. Amer. Math Soc. (to appear). MR**958897 (90e:16048)****[LP1]**-,*Etale local structure of matrixinvariants and concomitants*(Proc. Algebraic Groups Utrecht, 1986), Lecture Notes in Math., vol. 1271, Springer-Verlag 1987, pp. 143-176.**[Yu]**S. Yuan,*Modules and algebra classgroups over Noetherian integrally closed domains*, J. Algebra**32**(1974), 405-417. MR**0357463 (50:9931)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
16A46,
13A20,
14M20,
16A64,
20G15

Retrieve articles in all journals with MSC: 16A46, 13A20, 14M20, 16A64, 20G15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0931734-3

Keywords:
Invariant theory,
representations of quivers,
Brauer group

Article copyright:
© Copyright 1989
American Mathematical Society