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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dialgebra cohomology as a G-algebra


Authors: Anita Majumdar and Goutam Mukherjee
Journal: Trans. Amer. Math. Soc. 356 (2004), 2443-2457
MSC (2000): Primary 13D03, 17B63; Secondary 18G60
Published electronically: November 25, 2003
MathSciNet review: 2048524
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Abstract: It is well known that the Hochschild cohomology $H^*(A,A)$ of an associative algebra $A$ admits a G-algebra structure. In this paper we show that the dialgebra cohomology $HY^*(D,D)$ of an associative dialgebra $D$ has a similar structure, which is induced from a homotopy G-algebra structure on the dialgebra cochain complex $CY^*(D,D)$.


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Additional Information

Anita Majumdar
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata-700108, India
Email: anita_r@isical.ac.in

Goutam Mukherjee
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata-700108, India
Email: goutam@isical.ac.in

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03387-7
PII: S 0002-9947(03)03387-7
Keywords: Dialgebra, operad, brace algebra, homotopy G-algebra, G-algebra
Received by editor(s): September 27, 2002
Received by editor(s) in revised form: April 24, 2003
Published electronically: November 25, 2003
Additional Notes: The first author was supported by an N.B.H.M. Research Fellowship
Article copyright: © Copyright 2003 American Mathematical Society