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 Zap. Nauchn. Sem. POMI, 2015, Volume 437, Pages 5–14 (Mi znsl6170)

Group-graded systems and algebras

V. Arzumaniana, S. Grigoryanb

a Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Armenia
b Kazan State Power Engineering University, Kazan, Russia

Abstract: In the paper, we discuss some problems concerning the structural properties of crossed products. While expansions of $C^*$-algebras under group actions have been studied rather extensively, known difficulties in the transition to irreversible dynamical systems require the development of new methods. The first step in this direction is to study actions of inverse semigroups, whose properties are closest to those of groups. The main tool to achieve the goal is the concept of grading. The detection of the grading structure in the corresponding constructions seems to be very promising.

Key words and phrases: $C^*$-algebra, representation, conditional expectation, bimodule, Hilbert module, graded system, graded $C^*$-algebra, inverse semigroup.

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English version:
Journal of Mathematical Sciences (New York), 2016, 216:1, 1–7

Bibliographic databases:

UDC: 512.53+517.986.22+517.986.24
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Citation: V. Arzumanian, S. Grigoryan, “Group-graded systems and algebras”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Zap. Nauchn. Sem. POMI, 437, POMI, St. Petersburg, 2015, 5–14; J. Math. Sci. (N. Y.), 216:1 (2016), 1–7

Citation in format AMSBIB
\Bibitem{ArzGri15}
\by V.~Arzumanian, S.~Grigoryan
\paper Group-graded systems and algebras
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XXVI. Representation theory, dynamical systems, combinatorial methods
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 437
\pages 5--14
\publ POMI
\mathnet{http://mi.mathnet.ru/znsl6170}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3499905}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 216
\issue 1
\pages 1--7
\crossref{https://doi.org/10.1007/s10958-016-2883-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84969785522}