Smooth DG algebras and twisted tensor product
- Авторы: Орлов Д.О.1
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Учреждения:
- Математический институт им. В.А. Стеклова Российской академии наук
- Выпуск: Том 78, № 5 (2023)
- Страницы: 65-92
- Раздел: Статьи
- URL: https://medbiosci.ru/0042-1316/article/view/140491
- DOI: https://doi.org/10.4213/rm10139
- ID: 140491
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Аннотация
The twisted tensor product of DG algebras is studied and sufficient conditions for smoothness of such a product are presented. It is shown that in the case of finite-dimensional DG algebras, applying this operation offers great possibilities for constructing new examples of smooth DG algebras and algebras. In particular, examples are given of families of algebras of finite global dimension with two simple modules that have non-trivial moduli spaces. Bibliography: 24 titles.
Об авторах
Дмитрий Олегович Орлов
Математический институт им. В.А. Стеклова Российской академии наук
Email: orlov@mi-ras.ru
доктор физико-математических наук, без звания
Список литературы
- A. I. Bondal, M. Van den Bergh, “Generators and representability of functors in commutative and noncommutative geometry”, Mosc. Math. J., 3:1 (2003), 1–36
- D. A. Buell, Binary quadratic forms. Classical theory and modern computations, Springer-Verlag, New York, 1989, x+247 pp.
- A. Čap, H. Schichl, J. Vanžura, “On twisted tensor products of algebras”, Comm. Algebra, 23:12 (1995), 4701–4735
- Д. В. Дубнов, “О базисных алгебрах конечной гомологической размерности”, Вестн. Моск. ун-та. Сер. 1. Матем., мех., 1997, № 2, 15–17
- A. J. Efimov, “Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration”, Invent. Math., 222:2 (2020), 667–694
- A. Elagin, “Calculating dimension of triangulated categories: path algebras, their tensor powers and orbifold projective lines”, J. Algebra, 592 (2022), 357–401
- P. Gabriel, “Auslander–Reiten sequences and representation-finite algebras”, Representation theory (Carleton Univ., Ottawa, ON, 1979), v. I, Lecture Notes in Math., 831, Springer, Berlin, 1980, 1–71
- E. L. Green, “Remarks on projective resolutions”, Representation theory (Carleton Univ., Ottawa, ON, 1979), v. II, Lecture Notes in Math., 832, Springer, Berlin, 1980, 259–279
- D. Happel, “A family of algebras with two simple modules and Fibonacci numbers”, Arch. Math. (Basel), 57:2 (1991), 133–139
- D. Happel, D. Zacharia, “Algebras of finite global dimension”, Algebras, quivers and representations, Abel Symp., 8, Springer, Heidelberg, 2013, 95–113
- K. Igusa, “Notes on the no loops conjecture”, J. Pure Appl. Algebra, 69:2 (1990), 161–176
- B. Keller, “Deriving DG categories”, Ann. Sci. Ecole Norm. Sup. (4), 27:1 (1994), 63–102
- E. Kirkman, J. Kuzmanovich, “Algebras with large homological dimensions”, Proc. Amer. Math. Soc., 109:4 (1990), 903–906
- A. Kuznetsov, E. Shinder, Homologically finite-dimensional objects in triangulated categories, 2023 (v1 – 2022), 32 pp.
- Qunhua Liu, Dong Yang, “Stratifications of algebras with two simple modules”, Forum Math., 28:1 (2016), 175–188
- V. A. Lunts, “Categorical resolution of singularities”, J. Algebra, 323:10 (2010), 2977–3003
- V. A. Lunts, O. M. Schnürer, “Smoothness of equivariant derived categories”, Proc. Lond. Math. Soc. (3), 108:5 (2014), 1226–1276
- F. H. Membrillo-Hernandez, “Quasi-hereditary algebras with two simple modules and Fibonacci numbers”, Comm. Algebra, 22:11 (1994), 4499–4509
- D. Orlov, “Remarks on generators and dimensions of triangulated categories”, Mosc. Math. J., 9:1 (2009), 143–149
- D. Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105
- Д. О. Орлов, “Производные некоммутативные схемы, геометрические реализации и конечномерные алгебры”, УМН, 73:5(443) (2018), 123–182
- D. Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096, 33 pp.
- Д. О. Орлов, “Скрученные тензорные произведения ДГ алгебр”, УМН, 76:6(462) (2021), 199–200
- R. Rouquier, “Dimensions of triangulated categories”, J. K-Theory, 1:2 (2008), 193–256
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