Speciality:
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.
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
