Affine algebraic monoids as endomorphisms’ monoids of finite-dimensional algebras
HTML articles powered by AMS MathViewer
- by Alexander Perepechko PDF
- Proc. Amer. Math. Soc. 137 (2009), 3227-3233 Request permission
Abstract:
We prove that any affine algebraic monoid can be obtained as the endomorphisms’ monoid of a finite-dimensional (nonassociative) algebra.References
- Ivan V. Arzhantsev, Affine embeddings of homogeneous spaces, Surveys in geometry and number theory: reports on contemporary Russian mathematics, London Math. Soc. Lecture Note Ser., vol. 338, Cambridge Univ. Press, Cambridge, 2007, pp. 1–51. MR 2306139, DOI 10.1017/CBO9780511721472.002
- Nikolai L. Gordeev and Vladimir L. Popov, Automorphism groups of finite dimensional simple algebras, Ann. of Math. (2) 158 (2003), no. 3, 1041–1065. MR 2031860, DOI 10.4007/annals.2003.158.1041
- Mohan S. Putcha, Linear algebraic monoids, London Mathematical Society Lecture Note Series, vol. 133, Cambridge University Press, Cambridge, 1988. MR 964690, DOI 10.1017/CBO9780511600661
- Lex E. Renner, Linear algebraic monoids, Encyclopaedia of Mathematical Sciences, vol. 134, Springer-Verlag, Berlin, 2005. Invariant Theory and Algebraic Transformation Groups, V. MR 2134980
- A. Rittatore, Algebraic monoids and group embeddings, Transform. Groups 3 (1998), no. 4, 375–396. MR 1657536, DOI 10.1007/BF01234534
- E. B. Vinberg, On reductive algebraic semigroups, Lie groups and Lie algebras: E. B. Dynkin’s Seminar, Amer. Math. Soc. Transl. Ser. 2, vol. 169, Amer. Math. Soc., Providence, RI, 1995, pp. 145–182. MR 1364458, DOI 10.1090/trans2/169/10
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
- Received by editor(s): September 13, 2008
- Published electronically: May 27, 2009
- Communicated by: Birge Huisgen-Zimmermann
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2515393