NDLI: The Category and Operad of Matching Dialgebras

Content Provider	Springer Nature Link
Author	Guo, Li Bai, Chengming Zhang, Yong
Copyright Year	2012
Abstract	This paper gives a systematic study of matching dialgebras corresponding to the operad As (2) in Zinbiel (2012) as the only Koszul self dual operad there other than the operads of associative algebras and Poisson algebras. The close relationship of matching dialgebras with semi-homomorphisms and matched pairs of associative algebras are established. By anti-symmetrizing, matching dialgerbas are also shown to give compatible Lie algebras, pre-Lie algebras and PostLie algebras. By the rewriting method, the operad of matching dialgebras is shown to be Koszul and the free objects are constructed in terms of tensor algebras. The operadic complex computing the homology of the matching dialgebras is made explicit.
Ending Page	865
Page Count	15
Starting Page	851
File Format	PDF
ISSN	09272852
e-ISSN	15729095
Journal	Applied Categorical Structures
Issue Number	6
Volume Number	21
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-09-07
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quillen homology Matching dialgebra Theory of Computation Pre-Lie algebra Other (co)homology theories Operads Semi-direct sum Geometry PostLie algebra Convex and Discrete Geometry Free algebra Koszul operad Matched pairs Rewriting method Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Algebra and Number Theory Computer Science

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