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On existence of PI-exponents of codimension growth
1. | Department of Algebra, Faculty of Mathematics and Mechanics, Moscow State University, Moscow, 119992, Russian Federation |
References:
[1] |
Yu. A. Bahturin, Identical Relations in Lie Algebras, Translated from the Russian by Bahturin, VNU Science Press, b.v., Utrecht, 1987. |
[2] |
Yu. Bahturin and V. Drensky, Graded polynomial identities of matrices, Linear Algebra Appl., 357 (2002), 15-34.
doi: 10.1016/S0024-3795(02)00356-7. |
[3] |
F. Benanti and I. Sviridova, Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras, Israel J. Math., 156 (2006), 73-91.
doi: 10.1007/BF02773825. |
[4] |
A. Berele, Properties of hook Schur functions with applications to p.i. algebras, Adv. in Appl. Math., 41 (2008), 52-75.
doi: 10.1016/j.aam.2007.03.002. |
[5] |
A. Berele, An example concerning the constant in the asymptotics of codimension sequences, Comm. Algebra, 38 (2010), 3506-3510.
doi: 10.1080/00927870902939426. |
[6] |
A. Berele and A. Regev, Codimensions of products and of intersections of verbally prime T-ideals, Israel J. Math., 103 (1998), 17-28.
doi: 10.1007/BF02762265. |
[7] |
V. Drensky, Free Algebras and PI-Algebras, Graduate Course in Algebra, Springer-Verlag Singapore, Singapore, 2000. |
[8] |
A. S. Dzhumadil'daev, Codimension growth and non-Koszulity of Novikov operad, Comm. Algebra, 39 (2011), 2943-2952.
doi: 10.1080/00927870903386494. |
[9] |
A. Giambruno, I. Shestakov and M. Zaicev, Finite-dimensional non-associative algebras and codimension growth, Adv. in Appl. Math., 47 (2011), 125-139.
doi: 10.1016/j.aam.2010.04.007. |
[10] |
A. Giambruno and M. Zaicev, Exponential codimension growth of PI algebras: An exact estimate, Adv. Math., 142 (1999), 221-243.
doi: 10.1006/aima.1998.1790. |
[11] |
A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, 122, American Mathematical Society, Providence, RI, 2005.
doi: 10.1090/surv/122. |
[12] |
A. Giambruno and M. Zaicev, Codimension growth of special simple Jordan algebras, Trans. Amer. Math. Soc., 362 (2010), 3107-3123.
doi: 10.1090/S0002-9947-09-04865-X. |
[13] |
A. Giambruno and M. Zaicev, On codimension growth of finite-dimensional Lie superalgebras, J. Lond. Math. Soc. (2), 85 (2012), 534-548.
doi: 10.1112/jlms/jdr059. |
[14] |
A. R. Kemer, The Spechtian nature of T-ideals whose condimensions have power growth, (Russian) Sibirsk. Mat. Ž., 19 (1978), 54-69, 237. |
[15] |
D. Krakowski and A. Regev, The polynomial identities of the Grassmann algebra, Trans. Amer. Math. Soc., 181 (1973), 429-438. |
[16] |
V. N. Latyšev, On Regev's theorem on identities in a tensor product of PI-algebras, (Russian) Uspehi Mat. Nauk, 27 (1972), 213-214. |
[17] |
S. P. Mishchenko, Varieties of Lie algebras with weak growth of the sequence of codimensions, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1982, 63-66. |
[18] |
S. P. Mishchenko, Growth of varieties of Lie algebras, (Russian) Uspekhi Mat. Nauk, 45 (1990), 25-45, 189; translation in Russian Math. Surveys, 45 (1990), 27-52.
doi: 10.1070/RM1990v045n06ABEH002710. |
[19] |
S. P. Mishchenko and V. M. Petrogradsky, Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra, Comm. Algebra, 27 (1999), 2223-2230.
doi: 10.1080/00927879908826560. |
[20] |
S. P. Mishchenko, V. M. Petrogradsky and A. Regev, Poisson PI algebras, Trans. Amer. Math. Soc., 359 (2007), 4669-4694.
doi: 10.1090/S0002-9947-07-04008-1. |
[21] |
S. Mishchenko and A. Valenti, A Leibniz variety with almost polynomial growth, J. Pure Appl. Algebra, 202 (2005), 82-101.
doi: 10.1016/j.jpaa.2005.01.013. |
[22] |
D. Pagon, D. Repovš and M. Zaicev, On the codimension growth of simple color Lie superalgebras, J. Lie Theory, 22 (2012), 465-479. |
[23] |
A. Regev, Existence of identities in $A\otimes B$, Israel J. Math., 11 (1972), 131-152.
doi: 10.1007/BF02762615. |
[24] |
A. Regev, Codimensions and trace codimensions of matrices are asymptotically equal, Israel J. Math., 47 (1984), 246-250.
doi: 10.1007/BF02760520. |
[25] |
I. B. Volichenko, Varieties of Lie algebras with identity $[[x_1,x_2,x_3],$ $ [x_4,x_5,x_6]]$ $= 0$ over a field of characteristic zero, (Russian) Sibirsk. Mat. Zh., 25 (1984), 40-54. |
[26] |
M. V. Zaicev, Varieties and identities of affine Kac-Moody algebras, in Methods in Ring Theory (Levico Terme, 1997), Lecture Notes in Pure and Appl. Math., 198, Dekker, New York, 1998, 303-314. |
[27] |
M. V. Zaitsev, Integrality of exponents of growth of identities of finite-dimensional Lie algebras, (Russian) Izv. Ross. Akad. Nauk Ser. Mat., 66 (2002), 23-48; translation in Izv. Math., 66 (2002), 63-487.
doi: 10.1070/IM2002v066n03ABEH000386. |
[28] |
M. V. Zaitsev and S. P. Mishchenko, The growth of some varieties of Lie superalgebras, (Russian) Izv. Ross. Akad. Nauk Ser. Mat., 71 (2007), 3-18; translation in Izv. Math., 71 (2007), 657-672.
doi: 10.1070/IM2007v071n04ABEH002371. |
show all references
References:
[1] |
Yu. A. Bahturin, Identical Relations in Lie Algebras, Translated from the Russian by Bahturin, VNU Science Press, b.v., Utrecht, 1987. |
[2] |
Yu. Bahturin and V. Drensky, Graded polynomial identities of matrices, Linear Algebra Appl., 357 (2002), 15-34.
doi: 10.1016/S0024-3795(02)00356-7. |
[3] |
F. Benanti and I. Sviridova, Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras, Israel J. Math., 156 (2006), 73-91.
doi: 10.1007/BF02773825. |
[4] |
A. Berele, Properties of hook Schur functions with applications to p.i. algebras, Adv. in Appl. Math., 41 (2008), 52-75.
doi: 10.1016/j.aam.2007.03.002. |
[5] |
A. Berele, An example concerning the constant in the asymptotics of codimension sequences, Comm. Algebra, 38 (2010), 3506-3510.
doi: 10.1080/00927870902939426. |
[6] |
A. Berele and A. Regev, Codimensions of products and of intersections of verbally prime T-ideals, Israel J. Math., 103 (1998), 17-28.
doi: 10.1007/BF02762265. |
[7] |
V. Drensky, Free Algebras and PI-Algebras, Graduate Course in Algebra, Springer-Verlag Singapore, Singapore, 2000. |
[8] |
A. S. Dzhumadil'daev, Codimension growth and non-Koszulity of Novikov operad, Comm. Algebra, 39 (2011), 2943-2952.
doi: 10.1080/00927870903386494. |
[9] |
A. Giambruno, I. Shestakov and M. Zaicev, Finite-dimensional non-associative algebras and codimension growth, Adv. in Appl. Math., 47 (2011), 125-139.
doi: 10.1016/j.aam.2010.04.007. |
[10] |
A. Giambruno and M. Zaicev, Exponential codimension growth of PI algebras: An exact estimate, Adv. Math., 142 (1999), 221-243.
doi: 10.1006/aima.1998.1790. |
[11] |
A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Mathematical Surveys and Monographs, 122, American Mathematical Society, Providence, RI, 2005.
doi: 10.1090/surv/122. |
[12] |
A. Giambruno and M. Zaicev, Codimension growth of special simple Jordan algebras, Trans. Amer. Math. Soc., 362 (2010), 3107-3123.
doi: 10.1090/S0002-9947-09-04865-X. |
[13] |
A. Giambruno and M. Zaicev, On codimension growth of finite-dimensional Lie superalgebras, J. Lond. Math. Soc. (2), 85 (2012), 534-548.
doi: 10.1112/jlms/jdr059. |
[14] |
A. R. Kemer, The Spechtian nature of T-ideals whose condimensions have power growth, (Russian) Sibirsk. Mat. Ž., 19 (1978), 54-69, 237. |
[15] |
D. Krakowski and A. Regev, The polynomial identities of the Grassmann algebra, Trans. Amer. Math. Soc., 181 (1973), 429-438. |
[16] |
V. N. Latyšev, On Regev's theorem on identities in a tensor product of PI-algebras, (Russian) Uspehi Mat. Nauk, 27 (1972), 213-214. |
[17] |
S. P. Mishchenko, Varieties of Lie algebras with weak growth of the sequence of codimensions, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1982, 63-66. |
[18] |
S. P. Mishchenko, Growth of varieties of Lie algebras, (Russian) Uspekhi Mat. Nauk, 45 (1990), 25-45, 189; translation in Russian Math. Surveys, 45 (1990), 27-52.
doi: 10.1070/RM1990v045n06ABEH002710. |
[19] |
S. P. Mishchenko and V. M. Petrogradsky, Exponents of varieties of Lie algebras with a nilpotent commutator subalgebra, Comm. Algebra, 27 (1999), 2223-2230.
doi: 10.1080/00927879908826560. |
[20] |
S. P. Mishchenko, V. M. Petrogradsky and A. Regev, Poisson PI algebras, Trans. Amer. Math. Soc., 359 (2007), 4669-4694.
doi: 10.1090/S0002-9947-07-04008-1. |
[21] |
S. Mishchenko and A. Valenti, A Leibniz variety with almost polynomial growth, J. Pure Appl. Algebra, 202 (2005), 82-101.
doi: 10.1016/j.jpaa.2005.01.013. |
[22] |
D. Pagon, D. Repovš and M. Zaicev, On the codimension growth of simple color Lie superalgebras, J. Lie Theory, 22 (2012), 465-479. |
[23] |
A. Regev, Existence of identities in $A\otimes B$, Israel J. Math., 11 (1972), 131-152.
doi: 10.1007/BF02762615. |
[24] |
A. Regev, Codimensions and trace codimensions of matrices are asymptotically equal, Israel J. Math., 47 (1984), 246-250.
doi: 10.1007/BF02760520. |
[25] |
I. B. Volichenko, Varieties of Lie algebras with identity $[[x_1,x_2,x_3],$ $ [x_4,x_5,x_6]]$ $= 0$ over a field of characteristic zero, (Russian) Sibirsk. Mat. Zh., 25 (1984), 40-54. |
[26] |
M. V. Zaicev, Varieties and identities of affine Kac-Moody algebras, in Methods in Ring Theory (Levico Terme, 1997), Lecture Notes in Pure and Appl. Math., 198, Dekker, New York, 1998, 303-314. |
[27] |
M. V. Zaitsev, Integrality of exponents of growth of identities of finite-dimensional Lie algebras, (Russian) Izv. Ross. Akad. Nauk Ser. Mat., 66 (2002), 23-48; translation in Izv. Math., 66 (2002), 63-487.
doi: 10.1070/IM2002v066n03ABEH000386. |
[28] |
M. V. Zaitsev and S. P. Mishchenko, The growth of some varieties of Lie superalgebras, (Russian) Izv. Ross. Akad. Nauk Ser. Mat., 71 (2007), 3-18; translation in Izv. Math., 71 (2007), 657-672.
doi: 10.1070/IM2007v071n04ABEH002371. |
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