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Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities
Author(s):
Allan
Berele;
Amitai
Regev
Journal:
Trans. Amer. Math. Soc.
360
(2008),
5155-5172.
MSC (2000):
Primary 16R10
Posted:
May 27, 2008
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Additional information
Abstract:
Let  be a p. i. algebra with 1 in characteristic zero, satisfying a Capelli identity. Then the cocharacter sequence  is asymptotic to a function of the form  , where  and  .
References:
-
- 1.
- W. Beckner and A. Regev, Asymptotics and algebraicity of some generating functions, Adv. Math. 65 (1987), 1-15. MR 893467 (88h:05008)
- 2.
- W. Beckner and A. Regev, Asymptotic estimates using probability, Adv. Math. 138 (1998), 1-14. MR 1645060 (99j:05011)
- 3.
- A. Ya. Belov, Rationality of Hilbert series with respect to free algebras, Russian Math. Surveys 52 (1997), 394-395. MR 1480146 (98f:16018)
- 4.
- A. Berele, Approximate multiplicities in the trace cocharacter sequence of two three-by-three matrices,Comm. Algebra 25 (1997) 1975-1983. MR 1446144 (98j:05129)
- 5.
- A. Berele, Applications of Belov's theorem to the cocharacter sequence of p. i. algebras, J. of Alg. 298 (2006), 208-214. MR 2215124 (2006m:16023)
- 6.
- A. Berele and A. Regev, Codimensions of products and of intersections of verbally prime
 -ideals, Israel J. Math. 103 (1998), 17-28. MR 1613536 (99b:16037) - 7.
- A. Berele and A. Regev, Exponential growth for codimensions of some p. i. algebras, J. of Alg. 241 (2001), 118-145. MR 1838847 (2002k:16046)
- 8.
- V. Drensky, Codimensions of
 -ideals and Hilbert series of relatively free algebras, J. of Alg. 89 (1984), 178-223. MR 765766 (86b:16010) - 9.
- V. Drensky and G. K. Genov, Multiplicities of Schur functions in invariants of two
 matrices, J. Algebra 264 (2003), 496-519. MR 1981418 (2004c:16037) - 10.
- A. Giambruno and M. V. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998), 145-155. MR 1658530 (99k:16049)
- 11.
- A. Giambruno and M. V. Zaicev, Exponential codimension growth of PI algebras: An exact estimate, Adv. Math. 142 (1999), 221-243. MR 1680198 (2000a:16048)
- 12.
- B. Grünbaum, Convex Polytopes, Interscience, London, 1967. MR 0226496 (37:2085)
- 13.
- A. Guterman and A. Regev, On the growth of identities, In: Algebra (Moscow: 1998), 319-330, de Gruyter, Berlin, 2000. MR 1754678 (2001a:16039)
- 14.
- A. Regev, Asymptotic values for degrees associated with strips of Young diagrams, Adv. in Math. 41 (1981), 115-136. MR 625890 (82h:20015)
- 15.
- A. Regev, Algebras satisfying a Capelli identity, Israel J. Math. 33 (1979), 149-154. MR 571250 (81i:16022)
- 16.
- G. M. Zeigler, Lectures on Polytopes, Graduate Texts in Mathematics 152, Springer-Verlag, New York, 1995. MR 1311028 (96a:52011)
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Additional Information:
Allan
Berele
Affiliation:
Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email:
aberele@condor.depaul.edu
Amitai
Regev
Affiliation:
Department of Theoretical Mathematics, Weizmann Institute, Rehovot, Israel
Email:
amitai.regev@wisdom.weizmann.ac.il
DOI:
10.1090/S0002-9947-08-04500-5
PII:
S 0002-9947(08)04500-5
Keywords:
Polynomial identities,
cocharacter sequence
Received by editor(s):
June 5, 2006
Posted:
May 27, 2008
Additional Notes:
The work of the first author was supported by both the Faculty Research Council of DePaul University and the National Security Agency, under Grant MDA904-500270. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein.
The work of the second author was partially supported by ISF grant 947-04.
Copyright of article:
Copyright
2008,
American Mathematical Society
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