01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Keywords:
Banach modules; $C^*$-algebras; operator algebras; operator modules; homological theory of Banach and operator algebras; K-theory of $C^*$-algebras; noncommutative topology; Hopf-von Neumann algebras; Fourier algebra.
Subject:
Homology for algebras of analysis (Banach, locally convex, operator): homological epimorphisms, homological dimensions estimates, biprojectivity, approximate projectivity and flatness, Fouriier algebras and locally compact quantum groups.
Analysis on Lie groups: holomorphic functions of exponential type.
Noncommutative geometry: algebras of "noncommuting" smooth and analytic functions.
C*-algebras: tensor products, homotopic classification of simple algebras.
Banach spaces and modules: projective covers and radicals.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1991 (department of theory of functions and functional analysis). Ph.D. thesis 1995.
Main publications:
O. Yu. Aristov, “The global dimension theorem for non-unital and certain other separable $C^*$-algebras”, Sb. Math., 186:9 (1995), 1223–1239
O. Yu. Aristov, “On the homotopy equivalence of simple AI-algebras”, Sb. Math., 190:2 (1999), 165–191
O. Yu. Aristov, “Biprojective algebras and operator spaces”, Journal of Mathematical Sciences, 2002, 111, no. 2, 3369–3684
O. Yu. Aristov, “On approximation of flat Banach modules by free modules”, Sb. Math., 196:11 (2005), 1553–1583
O. Yu. Aristov, “Structure of biprojective Banach algebras with non-trivial radical”, Izv. Math., 72:6 (2008), 1111–1140
O. Yu. Aristov, “Holomorphic functions of exponential type on connected complex Lie groups”, J. Lie Theory, 29:4 (2019), 1045–10701903.08080
O. Yu. Aristov, “On holomorphic reflexivity conditions for complex Lie groups”, Proc. Edinburgh Math. Soc. (2), 64:4 (2021), 800–821 , arXiv: 2002.03617
O. Yu. Aristov, “Functions of class $C^\infty$ in non-commuting variables
in the context of triangular Lie algebras”, Izv. Math., 86:6 (2022), 1033–1071
O. Yu. Aristov, “Envelopes in the class of Banach algebras of polynomial growth and $C^\infty$-functions of a finite number of free variables”, arXiv: 2401.10199
2.
O. Yu. Aristov, “The Arens–Michael envelope of a solvable Lie algebra is a homological epimorphism” (Published online) , arXiv: 2404.19433
3.
O. Yu. Aristov, “Finitely $C^\infty$-generated associative and Hopf algebras” (to appear) , arXiv: 2408.11333
4.
O. Yu. Aristov, “Decomposition of the algebra of analytic functionals on a connected complex Lie group and its completions into iterated analytic smash products”, Algebra i Analiz, 36:4 (2024), 1–37 , arXiv: 2209.04192
5.
O. Yu. Aristov, “On density of polynomials in algebra of holomorphic functions of exponential type on linear Lie group”, Ufa Math. J., 16:2 (2024), 76–80 , arXiv: 2304.00507
O. Yu. Aristov, “When a completion of the universal enveloping algebra is a Banach PI-algebra?”, Bull. Aust. Math. Soc, 107:3 (2023), 493–501 , arXiv: 2204.07393
O. Yu. Aristov, “Length functions exponentially distorted on subgroups of complex Lie groups”, European Journal of Mathematics, 9 (2023), 60 (Published online) , arXiv: 2208.12667
O. Yu. Aristov, “The structure of the linearizer of a connected complex Lie group”, Siberian Math. J., 64:2 (2023), 287–290 , arXiv: 2203.04145
10.
O. Yu. Aristov, “Banach space representations of Drinfeld–Jimbo algebras and their complex-analytic forms”, Illinois J. Math., 67:2 (2023), 363-382 , arXiv: 2012.12565
11.
O. Yu. Aristov, “Sheaves of Noncommutative Smooth and Holomorphic Functions Associated with the Non-Abelian Two-Dimensional Lie Algebra”, Math. Notes, 112:1 (2022), 17–25
12.
O. Yu. Aristov, “Functions of class $C^\infty$ in non-commuting variables
in the context of triangular Lie algebras”, Izv. Math., 86:6 (2022), 1033–1071
13.
O. Yu. Aristov, “Holomorphic Reflexivity for Locally Finite and Profinite Groups: The Abelian and General Cases”, Math. Notes, 112:3 (2022), 339–348
14.
O. Yu. Aristov, “An analytic criterion for the local finiteness of a countable semigroup”, Siberian Math. J., 63:3 (2022), 421-424 , arXiv: 2104.03230
15.
O. Yu. Aristov, “The Relation “Commutator Equals Function” in Banach Algebras”, Math. Notes, 109:3 (2021), 323–334
16.
O. Yu .Aristov, A. Yu. Pirkovskii, “Corrigendum to “Open embeddings and pseudoflat epimorphisms” [J. Math. Anal. Appl. 485 (2020) 123817]”, J. Math. Anal. Appl., 2021, 125204
17.
O. Yu. Aristov, “On holomorphic reflexivity conditions for complex Lie groups”, Proc. Edinburgh Math. Soc. (2), 64:4 (2021), 800–821 , arXiv: 2002.03617
O. Yu. Aristov, “Arens–Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type and homological epimorphisms”, Trans. Moscow Math. Soc., 81:1 (2020), 97–114 , arXiv: arXiv: 1810.13213
21.
O. Yu. Aristov, “Holomorphic functions of exponential type on connected complex Lie groups”, J. Lie Theory, 29:4 (2019), 1045–10701903.08080
22.
O. Yu. Aristov, “Topological radical of a Banach module”, Studia Math., 234:2 (2016), 149–164
23.
Oleg Yu. Aristov, Volker Runde, Nico Spronk, Zsolt Tanko,, “Corrigendum to: “Operator biflatness of the Fourier algebra and approximate indicators for subgroups” [J. Funct. Anal. 209 (2) (2004) 367–387]”, Journal of Functional Analysis, 270:6 (2016), 2381–2382
24.
O. Yu. Aristov, “Structure of biprojective Banach algebras with non-trivial radical”, Izv. Math., 72:6 (2008), 1111–1140
25.
O. Yu. Aristov, “Projective covers of finitely generated Banach modules and the structure of some Banach algebras”, Extracta Math., 21:1 (2006), 1–26
26.
O. Yu. Aristov, “Fourier algebras of certain connected groups are not projective”, Russian Math. Surveys, 60:1 (2005), 154–156
27.
O. Yu. Aristov, “On approximation of flat Banach modules by free modules”, Sb. Math., 196:11 (2005), 1553–1583
28.
O. Yu. Aristov, “Amenability and compact type for Hopf-von Neumann algebras from the homological point of view”, Banach Algebras and Their Applications, Contemp. Math., 363, eds. A. T.-M. Lau and V. Runde,, 2004, 15–38
O. Yu. Aristov, V. Runde, N. Spronk, “Operator biflatness of the Fourier algebra and approximate indicators for subgroups”, Journal of Functional Analysis, 209:2 (2004), 367–387https://doi.org/10.1016/S0022-1236(03)00169-1
O. Yu. Aristov, “Biprojective algebras and operator spaces”, Journal of Mathematical Sciences, 2002, 111, no. 2, 3369–3684
31.
O. Yu. Aristov, “On tensor products of strict $C^*$-algebras”, Fundam. Prikl. Mat., 6:4 (2000), 977–984
32.
O. Yu. Aristov, “Homological dimensions of C*-algebras”, Topological Homology. Helemskii Moscow Seminar, eds. A.Ya. Helemskii, Nova Science Publishers, Huntington, N.Y., 2000, 39–56
33.
O. Yu. Aristov, “On the definition of a flat operator module”, Topological Homology. Helemskii Moscow Seminar, eds. A.Ya. Helemskii, Nova Science Publishers, Huntington, N.Y., 2000, 29–38
34.
O. Yu. Aristov, “On the homotopy equivalence of simple AI-algebras”, Sb. Math., 190:2 (1999), 165–191
35.
O. Yu. Aristov, “Representation of Schatten classes by operator algebras with the best homological properties”, in Russian, Function Theory, Applications and Adjacent questions, Kazan Math. Soc., Kazan, 1999, 21–24
36.
O. Yu. Aristov, “The global dimension theorem for non-unital and certain other separable $C^*$-algebras”, Sb. Math., 186:9 (1995), 1223–1239
37.
O. Yu. Aristov, “Characterization of strict C*-algebras”, Studia Math., 112:1 (1994), 51–58 DOI: 10.4064/sm-112-1-51-58
O. Yu. Aristov, “Nonvanishing of the secondary cohomologies of certain weakly amenable Banach algebras.”, Mosc. Univ. Math. Bull., 48:4 (1993), 46–48
Thesis
39.
O. Yu. Aristov, On certain homological and structural
characteristics of operator algebras, Ph.D. thesis (in Russian), Moscow State University, Moscow, 1995
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