index of elliptic operator,
$C^*$-algebra,
$C^*$-Hilbert module,
dynamical system,
conditional expectation,
irreducible representation,
Reidemeister number.
UDC:
517.98, 512.7, 517.986
Subject:
Noncommutative Geometry, Algebraic and Differential Topology, Functional Analysis, $K$-theory of $C^*$-algebras, index theory of elliptic operators, Noncommutative Harmonic Analysis, Group Theory.
Main publications:
Troitsky E., “Geometric essence of “compact” operators on Hilbert C*-modules”, Journal of Mathematical Analysis and Applications, 485 (2020), 123842
Felshtyn A., Troitsky E., “Twisted Burnside-Frobenius theory for discrete groups”, J. Reine Angew. Math. (Crelle's journal), 613 (2007), 193–210
Pavlov A.A., Troitsky E.V., “A $C^*$-analogue of Kazhdan's property (T)”, Adv. in Math., 216 (2007), 75–88
E. V. Troitskii, D. V. Fufaev, “Compact Operators and Uniform Structures in Hilbert $C^*$-Modules”, Funktsional. Anal. i Prilozhen., 54:4 (2020), 74–84; Funct. Anal. Appl., 54:4 (2020), 287–294
E. V. Troitskii, “Two examples related to the twisted Burnside–Frobenius theory for infinitely generated groups”, Fundam. Prikl. Mat., 21:5 (2016), 219–227; J. Math. Sci., 248:5 (2020), 661–666
A. A. Pavlov, E. V. Troitskii, “Property (T) for topological groups and $C^*$-algebras”, Fundam. Prikl. Mat., 13:8 (2007), 171–192; J. Math. Sci., 159:6 (2009), 863–878
E. V. Troitskii, “Noncommutative Riesz Theorem and Weak Burnside Type Theorem on Twisted Conjugacy”, Funktsional. Anal. i Prilozhen., 40:2 (2006), 44–54; Funct. Anal. Appl., 40:2 (2006), 117–125
E. V. Troitskii, “Thom isomorphism in the “twice” equivariant $K$-theory of $C^*$-fibrations”, Zap. Nauchn. Sem. POMI, 266 (2000), 245–253; J. Math. Sci. (N. Y.), 113:5 (2003), 683–688
1999
8.
E. V. Troitskii, “Actions of compact groups on algebras, the $C^*$-index theorem, and families”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 68 (1999), 129–188; J. Math. Sci. (New York), 105:2 (2001), 1884–1923
9.
E. V. Troitskii, “Functionals on $l_2(A)$, Kuiper and Dixmier–Douady Type Theorems for $C^*$-Hilbert Modules”, Trudy Mat. Inst. Steklova, 225 (1999), 362–380; Proc. Steklov Inst. Math., 225 (1999), 344–362
1998
10.
V. M. Manuilov, E. V. Troitskii, M. Frank, “Actions of groups and conditional expectations of finite index”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, no. 2, 30–34
1996
11.
E. V. Troitskii, M. Frank, “Lefschetz Numbers and Geometry of Operators in $W^*$-Modules”, Funktsional. Anal. i Prilozhen., 30:4 (1996), 45–57; Funct. Anal. Appl., 30:4 (1996), 257–266
E. V. Troitskii, “An Averaging Theorem in $C^*$-Hilbert Modules and Operators without Adjoint”, Funktsional. Anal. i Prilozhen., 28:3 (1994), 88–92; Funct. Anal. Appl., 28:3 (1994), 220–223
1993
13.
E. V. Troitskii, “The Hirzebruch operator on piecewise linear manifolds and highest signatures”, Uspekhi Mat. Nauk, 48:1(289) (1993), 189–190; Russian Math. Surveys, 48:1 (1993), 197–198
14.
E. V. Troitskii, “Traces, $C^*$-elliptic complexes, and higher-dimension even cyclic homology”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1993, no. 5, 36–39
1992
15.
E. V. Troitskii, “An exact formula for the index of an equivariant $C^*$-elliptic operator”, Trudy Mat. Inst. Steklov., 193 (1992), 178–182; Proc. Steklov Inst. Math., 193 (1993), 197–201
1989
16.
E. V. Troitskii, “Exact $K$-cohomological $C^*$-index formula. II. The index theorem and its applications”, Uspekhi Mat. Nauk, 44:1(265) (1989), 213–214; Russian Math. Surveys, 44:1 (1989), 259–260
1988
17.
E. V. Troitskii, “An exact $K$-cohomology $C^*$-index formula. I. Thom isomorphism and topological index”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, no. 2, 83–85
1986
18.
E. V. Troitskii, “Contractibility of the full general linear group of the $l_2(A)$”, Funktsional. Anal. i Prilozhen., 20:4 (1986), 58–64; Funct. Anal. Appl., 20:4 (1986), 301–307
E. V. Troitskii, “The equivariant index of $C^*$-elliptic operators”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 849–865; Math. USSR-Izv., 29:1 (1987), 207–224
E. V. Troitskii, “The index theorem for equivariant $C^*$-elliptic operators”, Dokl. Akad. Nauk SSSR, 282:5 (1985), 1059–1061
21.
E. V. Troitskii, “On the connection between complex and operator topological equivariant $K$-theories”, Uspekhi Mat. Nauk, 40:4(244) (1985), 227–228; Russian Math. Surveys, 40:4 (1985), 243–244
22.
E. V. Troitskii, “Classifying spaces for a $K$-functor connected with a $C^*$-algebra”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 1, 96–98
V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. Shavgulidze, “Yurii Petrovich Solov'ev (obituary)”, Uspekhi Mat. Nauk, 59:5(359) (2004), 135–140; Russian Math. Surveys, 59:5 (2004), 941–947
A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Uspekhi Mat. Nauk, 56:6(342) (2001), 167–170; Russian Math. Surveys, 56:6 (2001), 1187–1191
A. A. Irmatov, O. B. Lupanov, V. P. Maslov, V. M. Manuilov, A. A. Mikhalev, V. A. Sadovnichii, Yu. P. Solov'ev, E. V. Troitskii, A. T. Fomenko, “Aleksandr Sergeevitch Mischenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, no. 5, 67–69
Contact us: