Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Affine algebraic monoids as endomorphisms' monoids of finite-dimensional algebras


Author: Alexander Perepechko
Journal: Proc. Amer. Math. Soc. 137 (2009), 3227-3233
MSC (2000): Primary 17A36, 20M20; Secondary 16W22, 20G20
DOI: https://doi.org/10.1090/S0002-9939-09-09913-4
Published electronically: May 27, 2009
MathSciNet review: 2515393
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.


References [Enhancements On Off] (What's this?)

  • 1. I.V. Arzhantsev, Affine embeddings of homogeneous spaces, in ``Surveys in Geometry and Number Theory'', N. Young (Editor), London Math. Soc. Lecture Notes Series 338, Cambridge Univ. Press, Cambridge, 2007, 1-51. MR 2306139 (2008d:14074)
  • 2. N.L. Gordeev and V.L. Popov, Automorphism groups of finite dimensional simple algebras, Annals of Mathematics 158 (2003), 1041-1065. MR 2031860 (2005b:20086)
  • 3. M.S. Putcha, Linear algebraic monoids, London Math. Soc. Lecture Notes Series 133, Cambridge Univ. Press, Cambridge, 1988. MR 964690 (90a:20003)
  • 4. L. Renner, Linear algebraic monoids, Encyclopaedia of Mathematical Sciences 134, Springer-Verlag, Berlin-Heidelberg, 2005. MR 2134980 (2006a:20002)
  • 5. A. Rittatore, Algebraic monoids and affine embeddings, Transform. Groups 3 (1998), no. 4, 375-396. MR 1657536 (2000a:14056)
  • 6. E.B. Vinberg, On reductive algebraic semigroups, Amer. Math. Soc. Transl. (2) 169 (1995), 145-182. MR 1364458 (97d:20057)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 17A36, 20M20, 16W22, 20G20

Retrieve articles in all journals with MSC (2000): 17A36, 20M20, 16W22, 20G20


Additional Information

Alexander Perepechko
Affiliation: Department of Higher Algebra, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia
Email: perepechko@mccme.ru

DOI: https://doi.org/10.1090/S0002-9939-09-09913-4
Received by editor(s): September 13, 2008
Published electronically: May 27, 2009
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society