Abstract:
Let G be a compact Lie group, and A a C∗-algebra with identity.
A K-theory of G-equivariant A-vector bundles is developed along with a corresponding theory of Fredholm operators, and the analytic and topological indices of an elliptic equivariant pseudodifferential operator over a C∗-algebra A are defined. An index theorem generalizing the Mishchenko–Fomenko theorem is proved.
Bibliography: 19 titles.
\Bibitem{Tro86}
\by E.~V.~Troitskii
\paper The equivariant index of $C^*$-elliptic operators
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 207--224
\mathnet{http://mi.mathnet.ru/eng/im1538}
\crossref{https://doi.org/10.1070/IM1987v029n01ABEH000967}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=864180}
\zmath{https://zbmath.org/?q=an:0641.46047}
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https://www.mathnet.ru/eng/im1538
https://doi.org/10.1070/IM1987v029n01ABEH000967
https://www.mathnet.ru/eng/im/v50/i4/p849
This publication is cited in the following 4 articles:
L. V. Kuz'min, T. S. Fofanova, M. Sh. Tsalenko, A. B. Ivanov, V. L. Popov, L. N. Shevrin, V. N. Grishin, M. M. Lavrent'ev, P. S. Soltan, N. M. Nagornyǐ, L. A. Bokut', S. M. Nikol'skiǐ, A. V. Chernavskiǐ, S. Z. Shefel', A. G. Dragalin, V. A. Dushskiǐ, S. K. Sobolev, V. E. Plisko, L. D. Kudryavtsev, V. I. Danilov, V. A. Trenogin, N. N. Vil'yams, M. I. Voǐtsekhovskiǐ, V. E. Tarakanov, S. A. Rukova, V. I. Pagurova, I. V. Ostrovskiǐ, A. I. Shtern, Yu. V. Prokhorov, D. V. Anosov, S. A. Stepanov, M. A. Shubin, V. I. Zaǐtsev, M. S. Nikulin, D. D. Sokolov, D. P. Zhelobenko, M. A. Naǐmark, B. A. Pasynkov, E. B. Yanovskaya, E. D. Solomentsev, P. M. Tamrazov, Ü. Lumiste, A. N. Kolmogorov, N. N. Chentsov, R. L. Dobrushin, V. V. Prelov, A. V. Prokhorov, I. N. Vrublevskaya, V. M. Tikhomirov, A. V. Mikhalev, A. A. Tuganbaev, I. V. Dolgachev, E. G. Gol'shteǐn, E. V. Levner, V. A. Il'in, N. N. Ladis, B, Encyclopaedia of Mathematics, 1995, 123
E. V. Troitskii, “An Averaging Theorem in C∗-Hilbert Modules and Operators without Adjoint”, Funct. Anal. Appl., 28:3 (1994), 220–223
Jonathan Rosenberg, Shmuel Weinberger, “HigherG-signatures for Lipschitz manifolds”, K-Theory, 7:2 (1993), 101
E. V. Troitskii, “Exact K-cohomological C∗-index formula. II. The index theorem and its applications”, Russian Math. Surveys, 44:1 (1989), 259–260
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