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Ni, Xiang and Bai, Chengming (2012) Octo-bialgebras. Algebra Colloquium, 19 (2). pp. 305-332. ISSN 1005-3867.

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The notion of octo-algebra was introduced by Leroux as a Loday algebra with 8 operations. In this paper, we introduce a notion of octo-bialgebra as a bialgebra theory of octo-algebras, which is equivalent to a double construction of a quadri-algebra with a nondegenerate 2-cocycle or a double construction of an octo-algebra with a nondegenerate invariant bilinear form. Some properties of octo-bialgebras are given, including the study of the coboundary cases which leads to a construction from an analogue of the classical Yang-Baxter equation in an octo-algebra.

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Additional Information:© 2012 World Scientific Publishing Co. This work was supported in part by the NSFC (10621101, 10921061), NKBRPC (2006CB, 805905), and SRFDP (200800550015).
Funding AgencyGrant Number
NSFC (China)10621101
NSFC (China)10921061
Subject Keywords:Loday algebra, octo-algebra, quadri-algebra, classical Yang-Baxter equation
Issue or Number:2
Classification Code:2000 MSC: 16W30, 17A30, 18D50
Record Number:CaltechAUTHORS:20120509-100002672
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Official Citation:Octo-bialgebras Xiang Ni and Chengming Bai Page: 305-332
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31372
Deposited By: Ruth Sustaita
Deposited On:09 May 2012 17:36
Last Modified:03 Oct 2019 03:51

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