La Mattina, Daniela:
Varieties of Algebras of Polynomial Growth
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 525-538, (English)
pdf (390 Kb), djvu (137 Kb). | MR 2455329 | Zbl 1204.16019
Sunto
Let $\mathcal{V}$ be a proper variety of associative algebras over a field $F$ of characteristic zero. It is well-known that $\mathcal{V}$ can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of $\operatorname{\textbf{var}}(G)$ and $\operatorname{\textbf{var}}(UT_2)$, where $G$ is the Grassmann algebra and $UT_2$ is the algebra of $2 \times 2$ upper triangular matrices.
Referenze Bibliografiche
[2]
V. DRENSKY,
Relations for the cocharacter sequences of T-ideals,
Proceedings of the International Conference on Algebra, Part 2 (Novosibirsk, 1989), 285-300,
Contemp. Math.,
131,
Amer. Math. Soc., Providence, RI,
1992. |
MR 1175839 |
Zbl 0766.16012[3]
V. DRENSKY,
Free algebras and PI-algebras, Graduate course in algebra,
Springer-Verlag Singapore, Singapore,
2000. |
MR 1712064 |
Zbl 0936.16001[9]
A. GIAMBRUNO -
M. ZAICEV,
A characterization of algebras with polynomial growth of the codimensions,
Proc. Amer. Math. Soc.,
129 (
2000), 59-67. |
fulltext (doi) |
MR 1694862 |
Zbl 0962.16018[11]
A. GIAMBRUNO -
M. ZAICEV,
Polynomial Identities and Asymptotic Methods,
Mathematical Surveys and Monographs Vol.
122,
Amer. Math. Soc., Providence R.I.,
2005. |
fulltext (doi) |
MR 2176105 |
Zbl 1105.16001[12]
A. GUTERMAN -
A. REGEV,
On the growth of identities,
Algebra (Moscow, 1998) de Gruyter, Berlin, (
2000), 319-330. |
MR 1754678 |
Zbl 0964.16025[13]
A. R. KEMER,
T-ideals with power growth of the codimensions are Specht,
Sibirsk. Mat. Zh.,
19 (
1978), 54-69 (in Russian), English translation:
Sib. Math. J.,
19 (
1978), 37-48. |
MR 466190 |
Zbl 0411.16014[14] A. R. KEMER, Varieties of finite rank., Proc. 15-th All the Union Algebraic Conf., Krasnoyarsk, Vol. 2 (1979), 73 (in Russian).
[17]
YU. N. MALTSEV,
A basis for the identities of the algebra of upper triangular matrices, (Russian)
Algebra i Logika,
10 (
1971), 242-247. |
MR 304426