PI-exponents of some simple algebras with unit. (English. Russian original) Zbl 1378.17001
J. Math. Sci., New York 206, No. 6, 688-693 (2015); translation from Fundam. Prikl. Mat. 18, No. 4, 121-128 (2013).
Summary: Over a field of characteristic zero we have constructed a discrete series of simple finite-dimensional algebras with unit. Its sequence of dimensions is not bounded, but PI-exponents are different fractional numbers strictly less than 4.
MSC:
| 17A01 | General theory of nonassociative rings and algebras |
References:
| [1] | A. Giambruno, S. Mishchenko, and M. Zaicev, “Algebras with intermediate growth of the codimensions,” Adv. Appl. Math., 37, No. 3, 360-377 (2006). · Zbl 1111.16022 · doi:10.1016/j.aam.2005.02.005 |
| [2] | A. Giambruno, A. Regev, and M. Zaicev, “Simple and semisimple Lie algebras and codimension growth,” Trans. Am. Math. Soc., 352, No. 4, 1935-1946 (2000). · Zbl 0970.17004 · doi:10.1090/S0002-9947-99-02419-8 |
| [3] | A. Giambruno, I. Shestakov, and M. Zaicev, “Finite dimensional nonassociative algebras and codimension growth,” Adv. Appl. Math., No. 47, 125-139 (2011). · Zbl 1290.17028 |
| [4] | A. Giambruno and M. Zaicev, “Exponential codimension growth of P.I. algebras: an exact estimate,” Adv. Math., 142, 221-243 (1998). · Zbl 0920.16013 · doi:10.1006/aima.1998.1790 |
| [5] | A. Giambruno and M. Zaicev, “On codimension growth of finitely generated associative algebras,” Adv. Math., 140, 145-155 (1998). · Zbl 0920.16012 · doi:10.1006/aima.1998.1766 |
| [6] | A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Math. Surveys Monographs, Vol. 122, Amer. Math. Soc., Providence (2005). · Zbl 1105.16001 |
| [7] | A. Giambruno and M. Zaicev, “Codimension growth of special simple Jordan algebras,” Trans. Am. Math. Soc., 362, No. 6, 3107-3123 (2010). · Zbl 1205.17032 · doi:10.1090/S0002-9947-09-04865-X |
| [8] | O. A. Malyusheva, S. P. Mishchenko, and A. B. Verevkin, “The Lie algebras varieties series of different fractional exponents,” Dokl. Bolg. Akad. Nauk, 66, No. 3, 321-330 (2013). · Zbl 1313.17011 |
| [9] | M. V. Zaicev, “Integrality of exponents of growth of identities of finite-dimensional Lie algebras,” Izv. Math., 66, 463-487 (2002). · Zbl 1057.17003 · doi:10.1070/IM2002v066n03ABEH000386 |
| [10] | M. V. Zaicev, “Identities of finite dimensional unitary algebras,” Algebra Logika, 50, No. 5, 563-594 (2011). · Zbl 1273.16020 |
| [11] | M. V. Zaicev and D. Repovsh, “Four-dimensional simple algebra with fractional PI-exponent,” Math. Notes, 95, No. 4, 538-553 (2014). · Zbl 1387.17003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
