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2010

Additive Deformations of Hopf Algebras

Gerhold, Malte

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Understand

Additive deformations of bialgebras in the sense of Wirth are deformations of the multiplication map of the bialgebra fulfilling a compatibility condition with the coalgebra structure and a continuity condition.

Two problems concerning additive deformations are considered.
With a deformation theory a cohomology theory should be developed.
Here a variant of the Hochschild cohomology is used.

Additive Deformations of Hopf Algebras · Around

Built on

The cohomology structure of an associative ring
M. Gerstenhaber · 1963
Earlier work this paper cites.
On the deformation of rings and algebras
M. Gerstenhaber · 1964
Earlier work this paper cites.
Hopf algebras
M. E. Sweedler · 1969
Earlier work this paper cites.
Hopf algebras
E. Abe · 1980
Earlier work this paper cites.

Similar

Quantum independent increment processes on superalgebras
L. Accardi, M. Schürmann, and W. von Waldenfels · 1988
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Foundations of quantum group theory
S. Majid · 1995
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Quantum groups and their representations
A. Klimyk and K. Schmüdgen · 1997
Cited alongside, same era.

Then

Formule de Lévy Khintchine et deformations d’algebres
Original
J. Wirth · 2002
Later among the works it cites.
Lévy processes on deformations of Hopf algebras
M. Schürmann · 2005
Later among the works it cites.
Quanten-Lévy-Prozesse auf Deformationen von Bialgebren
M. Gerhold · 2009
Later among the works it cites.

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