Codimensions of identities of solvable Lie superalgebras
- Authors: Zaicev M.V.1, Repovš D.D.2
-
Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- University of Ljubljana
- Issue: Vol 88, No 4 (2024)
- Pages: 44-60
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/261164
- DOI: https://doi.org/10.4213/im9560
- ID: 261164
Cite item
Open Access
Access granted
Subscription Access
Abstract
Identities of Lie superalgebas over a field of characteristic zero are studied. The series of finite dimensional solvable Lie superalgebras with an integer PI-exponent of codimension growth is constructed.
Keywords
About the authors
Mikhail Vladimirovich Zaicev
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: zaicevmv@mail.ru
Doctor of physico-mathematical sciences, Professor
Dušan D.. Repovš
University of Ljubljana
Email: dusan.repovs@guest.arnes.si
ORCID iD: 0000-0002-6643-1271
SPIN-code: 2281-6131
Scopus Author ID: 7004606901
ResearcherId: C-3602-2008
PhD, Professor
References
- И. Б. Воличенко, “Многообразия алгебр Ли с тождеством $[[X_1,X_2,X_3],[X_4,X_5,X_6]]=0$ над полем характеристики нуль”, Сиб. матем. журн., 25:3 (1984), 40–54
- A. Regev, “Existence of identities in $Aotimes B$”, Israel J. Math., 11 (1972), 131–152
- В. Н. Латышев, “К теореме Регева о тождествах тензорного произведения $PI$-алгебр”, УМН, 27:4(166) (1972), 213–214
- Yu. Bahturin, V. Drensky, “Graded polynomial identities of matrices”, Linear Algebra Appl., 357:1-3 (2002), 15–34
- A. Giambruno, M. Zaicev, “Codimension growth of special simple Jordan algebras”, Trans. Amer. Math. Soc., 362:6 (2010), 3107–3123
- С. П. Мищенко, “Рост многообразий алгебр Ли”, УМН, 45:6(276) (1990), 25–45
- М. В. Зайцев, “Многообразия аффинных алгебр Каца–Муди”, Матем. заметки, 62:1 (1997), 95–102
- М. В. Зайцев, С. П. Мищенко, “Тождества супералгебр Ли с нильпотентным коммутантом”, Алгебра и логика, 47:5 (2008), 617–645
- A. S. Dzhumadil'daev, “Codimension growth and non-Koszulity of Novikov operad”, Comm. Algebra, 39:8 (2011), 2943–2952
- A. Giambruno, M. Zaicev, “On codimension growth of finitely generated associative algebras”, Adv. Math., 140:2 (1998), 145–155
- A. Giambruno, M. Zaicev, “Exponential codimension growth of PI algebras: an exact estimate”, Adv. Math., 142:2 (1999), 221–243
- М. В. Зайцев, “Целочисленность экспонент роста тождеств конечномерных алгебр Ли”, Изв. РАН. Сер. матем., 66:3 (2002), 23–48
- A. Giambruno, I. Shestakov, M. Zaicev, “Finite-dimensional non-associative algebras and codimension growth”, Adv. in Appl. Math., 47:1 (2011), 125–139
- A. Giambruno, M. Zaicev, “On codimension growth of finite-dimensional Lie superalgebras”, J. Lond. Math. Soc. (2), 85:2 (2012), 534–548
- D. Repovš, M. Zaicev, “Graded identities of some simple Lie superalgebras”, Algebr. Represent. Theory, 17:5 (2014), 1401–1412
- D. Repovš, M. Zaicev, “Graded codimensions of Lie superalgebra $b(2)$”, J. Algebra, 422 (2015), 1–10
- D. D. Repovš, M. V. Zaicev, “Codimension growth of solvable Lie superalgebras”, J. Lie Theory, 28:4 (2018), 1189–1199
- Ю. А. Бахтурин, Тождества в алгебрах Ли, Наука, М., 1985, 448 с.
- V. Drensky, Free algebras and PI-algebras. Graduate course in algebra, Springer-Verlag, Singapore, 2000, xii+271 pp.
- A. Giambruno, M. Zaicev, Polynomial identities and asymptotic methods, Math. Surveys Monogr., 122, Amer. Math. Soc., Providence, RI, 2005, xiv+352 pp.
- Г. Джеймс, Теория представлений симметрических групп, Мир, М., 1982, 216 с.
- М. В. Зайцев, “Градуированные тождества конечномерных алгебр коразмерностей тождеств ассоциативных алгебр”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 2015, № 5, 54–57
- M. Scheunert, The theory of Lie superalgebras. An introduction, Lecture Notes in Math., 716, Springer, Berlin, 1979, x+271 pp.
- O. M. Di Vincenzo, P. Koshlukov, R. La Scala, “Involutions for upper triangular matrix algebras”, Adv. in Appl. Math., 37:4 (2006), 541–568
