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Affine algebraic monoids as endomorphisms' monoids of finite-dimensional algebras
Author(s):
Alexander
Perepechko
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3227-3233.
MSC (2000):
Primary 17A36, 20M20;
Secondary 16W22, 20G20
Posted:
May 27, 2009
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Abstract:
We prove that any affine algebraic monoid can be obtained as the endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.
References:
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- 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)
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- 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)
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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:
10.1090/S0002-9939-09-09913-4
PII:
S 0002-9939(09)09913-4
Received by editor(s):
September 13, 2008
Posted:
May 27, 2009
Communicated by:
Birge Huisgen-Zimmermann
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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