Crossed product of a C*-algebra by a semigroup of interactions

• Autorzy: Kwaśniewski B. K.
• Języki publikacji: EN

Abstrakty

EN

The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev’s crossed product by an endomorphism, and is related to Exel’s interactions. One of the main goals is the Isomorphism Theorem established in the case of actions by endomorphisms.

Słowa kluczowe

EN

C*-algebra; interactions; partial isometry; crossed product; finely representable action; transfer operator

PL

C*-algebra; interakcje; częściowa izometria; operator przeniesienia

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 2
• Strony: 352--370
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Kwaśniewski B. K.

• Institute of Mathematics, University in Białystok, ul. Akademicka 2, PL-15-267 Białystok, Poland
• Institute of Mathematics, Polish Academy of Science, ul. Sniadeckich 2, PL-00-656 Warsaw, Poland

Bibliografia

• [1] A. B. Antonevich, V. I. Bakhtin, A. V. Lebedev, Crossed product of C*-algebra by an endomorphism, coefficient algebras and transfer operators, Mat. Sb. 202(9) (2011), 1253–1283.
• [2] A. B. Antonevich, A. V. Lebedev, Functional Differential Equations: I. C*-Theory, Longman Scientific & Technical, Pitman Monographs and Surveys in Pure and Applied Mathematics 70, 1994.
• [3] V. I. Bakhtin, A. V. Lebedev, When a C*-algebra is a coefficient algebra for a given endomorphism, preprint. arXiv:math.OA/0502414
• [4] J. Cuntz, Simple C*-algebras generated by isometries, Comm. Math. Phys. 57 (1977), 173–185.
• [5] J. Cuntz, W. Krieger, A class of C*-algebras and topological Markov chains, Invent. Math. 56 (1980), 251–268.
• [6] J. Dixmier, Les C*-Algebres et leurs Representations, Gauthier-Villars Editeur, 1969.
• [7] R. Exel, Circle actions on C*-algebras, partial automorhisms and generalized Pimsner–Voiculescu exact sequence, J. Funct. Anal. 122 (1994), 361–401.
• [8] R. Exel, A new look at the crossed-product of a C*-algebra by an endomorphism, Ergodic Theory Dynam. Systems 23 (2003), 1733–1750.
• [9] R. Exel, Interactions, J. Funct. Anal. 244 (2007), 26–62.
• [10] P. R. Halmos, L. J. Wallen, Powers of partial isometries, Indiana Univ. Math. J. 19 (1970), 657–663.
• [11] B. K. Kwasniewski, Covariance algebra of a partial dynamical system, Cent. Eur. J. Math. 3(4) (2005), 718–765.
• [12] B. K. Kwasniewski, A. V. Lebedev, Crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries, Integral Equations Operator Theory 63 (2009), 403–425.
• [13] N. S. Larsen, Crossed products by abelian semigroups via transfer operators, Ergodic Theory Dynam. Systems 30 (2010), 1147–1164.
• [14] A. V. Lebedev, Topologically free partial actions and faithful representations of partial crossed products, Funct. Anal. Appl. 39(3) (2005), 207–214.
• [15] A. V. Lebedev, A. Odzijewicz, Extensions of C*-algebras by partial isometries, Mat. Sb. 195(7) (2004), 37–70.
• [16] G. J. Murphy, Crossed products of C*-algebras by endomorphisms, Integr. Equ. Oper. Theory 24(1996), 298–319.
• [17] G. J. Murphy, C*-Algebras and Operator Theory, Academic Press, 1990.
• [18] W. L. Paschke, The crossed product of a C*-algebra by an endomorphism, Proc. Amer. Math. Soc. 80(1) (1980), 113–118.
• [19] J. Tomiyama, Invitation to C*-Algebras and Topological Dynamics, World Scientific, 1987.