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International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 7, Pages 429-438

Reflexive and dihedral (co)homology of a pre-additive category

Department of Mathematics, Faculty of Science, South Valley University, Aswan, Egypt

Received 18 June 1998

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The group dihedral homology of an algebra over a field with characteristic zero was introduced by Tsygan (1983). The dihedral homology and cohomology of an algebra with involution over commutative ring with identity, associated with the small category, were studied by Krasauskas et al. (1988), Loday (1987), and Lodder (1993). The aim of this work is concerned with dihedral and reflexive (co)homology of small pre-additive category. We also define the free product of involutive algebras associated with this category and study its dihedral homology group. Finally, following Perelygin (1990), we show that a small pre-additive category is Morita equivalence.