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ON THE TOTAL COMPONENT OF THE PARTIAL SCHUR MULTIPLIER

Part of: Representation theory of groups Semigroups

Published online by Cambridge University Press:  26 February 2016

H. G. G. DE LIMA  and
H. PINEDO
H. G. G. DE LIMA
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010 05508-090 São Paulo, SP, Brasil email [email protected]
H. PINEDO*
Affiliation:
Escuela de Matemáticas, Universidad Industrial de Santander, Cra 27 calle 9, Bucaramanga, Santander, Colombia email [email protected]
*
✉[email protected]
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Abstract

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In this paper we determine the structure of the total component of the Schur multiplier over an algebraically closed field of some relevant families of groups, such as dihedral groups, dicyclic groups, the infinite cyclic group and the direct product of two finite cyclic groups.

Keywords

partial Schur multiplierfactor settotal component

MSC classification

Primary: 20C25: Projective representations and multipliers
Secondary: 20M30: Representation of semigroups; actions of semigroups on sets 20M50: Connections of semigroups with homological algebra and category theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 3 , June 2016 , pp. 374 - 402
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Clifford, A. H. and Preston, B., The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys and Monographs, 7 (American Mathematical Society, Providence, RI, 1961).CrossRefGoogle Scholar
Dokuchaev, M., Exel, R. and Piccione, P., ‘Partial representations and partial group algebras’, J. Algebra 226 (2000), 502–532.Google Scholar
Dokuchaev, M. and Novikov, B., ‘Partial projective representations and partial actions’, J. Pure Appl. Algebra 214 (2010), 251–268.Google Scholar
Dokuchaev, M. and Novikov, B., ‘Partial projective representations and partial actions II’, J. Pure Appl. Algebra 216 (2012), 438–455.Google Scholar
Dokuchaev, M., Novikov, B. and Pinedo, H., ‘The partial Schur multiplier of a group’, J. Algebra 392 (2013), 199–225.CrossRefGoogle Scholar
Dokuchaev, M., Pinedo, H. and de Lima, H. G. G., ‘Partial representations and their domains’, Preprint, 2014.Google Scholar
Exel, R., ‘Partial actions of groups and actions of inverse semigroups’, Proc. Amer. Math. Soc. 126 (1998), 3481–3494.Google Scholar
Novikov, B. and Pinedo, H., ‘On components of the partial Schur multiplier’, Comm. Algebra 42(6) (2014), 2484–2495.Google Scholar
Pinedo, H., ‘On elementary domains of partial projective representations of groups’, Algebra Discrete Math. 15(1) (2013), 63–82.Google Scholar
Pinedo, H., ‘A calculation of the partial Schur multiplier of S 3’, Int. J. Math. Game Theory Algebra 22(4) (2014), 405–417.Google Scholar