Homology theory for Banach and topological algebras.
Biography
Graduated from Moscow State University, Department of Mechanics and Mathematics (1997). PhD in Mathematics (2000). Teaching at Peoples' Friendship University of Russia and at Independent University of Moscow. Research interests: homology theory for Banach and topological algebras and its applications in spectral theory and in noncommutative geometry.
Main publications
Pirkovskii, A. Yu. On the conditions ensuring the freedom of topological modules over algebras of holomorphic functions (in Russian). Fund. i Prikl. Matem. 4 (1998), No. 2, 585–594.
Pirkovskii, A. Yu. On the problem of the existence of a sufficient number of injective Fréchet modules over nonnormable Fréchet algebras (in Russian). Izvestiya Ross. Akad. Nauk, ser. matem. 62 (1998), No. 4, 137–154. English transl.: Izvestiya: Mathematics 62 (1998), No. 4, 773–788.
Pirkovskii A. Yu. On the nonexistence of cofree Fréchet modules over locally multiplicatively-convex Fréchet algebras. Rocky Mountain J. Math. 29 (1999), No. 3, 1129–1138.
Pirkovskii A. Yu. On Arens–Michael algebras which do not have nonzero injective $\mathop{\widehat{\otimes}}$-modules. Studia Math. 133 (1999), No. 2, 163–174.
Pirkovskii, A. Yu. On certain homological properties of Stein algebras. Functional analysis, 3. J. Math. Sci. (New York) 95 (1999), no. 6, 2690–2702.
Pirkovskii A. Yu. Injective topological modules, additivity formulas for homological dimensions, and related topics. Topological Homology: Helemskii's Moscow Seminar (ed. A. Ya. Helemskii), 93–143, Nova Science Publishers, Inc., Huntington, NY, 2000.
Pirkovskii, A. Yu. Some results on injective topological modules and injective homological dimensions. Topological Algebras with Applications to Differential Geometry and Mathematical Physics, Proceedings of the Fest-Colloquium in Honour of A. Mallios, Athens, September 1999, 72–85. Athens University Publ., Athens, 2002.
Pirkovskii, A. Yu. Biprojective topological algebras of homological bidimension 1. J. Math. Sci. (New York) 111 (2002), No. 2, 3476–3495.
Pirkovskii, A. Yu. Homological bidimension of biprojective topological algebras and nuclearity.
Proc. of the 3rd International Conference on Topological Algebra and Applications, Oulu University, Oulu, Finland, July 2–6, 2001; Acta Universitatis Ouluensis A 408 (2004), 179–196.
Pirkovskii, A. Yu. Biprojectivity and biflatness for convolution algebras of nuclear operators. Canad. Math. Bull. 47 (2004), no. 3, 445–455.
Pirkovskii, A. Yu. Arens–Michael enveloping algebras and analytic smash products. Proc. Amer. Math. Soc. 134 (2006), no. 9, 2621–2631.
12. Pirkovskii, A. Yu. Stably flat completions of universal enveloping algebras. Dissertationes Math. (Rozprawy Math.) 441 (2006), 1–60.
Pirkovskii, A. Yu., Selivanov, Yu. V. Homologically trivial Fréchet algebras. Proc. of the 5th International Conference on Topological Algebras and Applications, Athens, 2005. Contemporary Math. 427 (2007), 367–387.
Pirkovskii, A. Yu. Strictly flat cyclic Fréchet modules and approximate identities. Proc. of the 5th International Conference on Topological Algebras and Applications, Athens, 2005. Contemporary Math. 427 (2007), 359–366.
Pirkovskii, A. Yu. Approximate characterizations of projectivity and injectivity for Banach modules. Math. Proc. Cambridge Phil. Soc. 143 (2007), no. 2, 375-385.
Pirkovskii, A. Yu. Weak homological dimensions and biflat K\"othe algebras (in Russian). Sbornik: Mathematics, 2008, 199:5, 45-80.
Pirkovskii, A. Yu. Arens-Michael envelopes, homological epimorphisms, and relatively quasi-free algebras. Trans. Moscow Math. Soc., to appear (2008).
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