Michael Penkava
The moduli space of $1|2$-dimensional complex associative algebras.
Mon, 11/02/2009 - 16:01 — SomNambulAuthors: Michael Penkava, Chris DeCleene, Carolyn Otto, Mitch Phillipson, Ryan Steinbach, Eric Weber
Subjects: Rings and Algebras
AbstractIn this paper, we study the moduli space of $1|2$-dimensional complex
associative algebras, which is also the moduli space of codifferentials on the
tensor coalgebra of a $2|1$-dimensional complex space. We construct the moduli
space by considering extensions of lower dimensional algebras. We also
construct miniversal deformations of these algebras. This gives a complete
description of how the moduli space is glued together via jump deformations.The moduli space of $2|1$-dimensional complex associative algebras.
Mon, 10/26/2009 - 14:11 — SomNambulAuthors: Michael Penkava, Chris DeCleene, Carolyn Otto, Mitch Phillipson, Ryan Steinbach, Eric Weber
Subjects: Rings and Algebras
AbstractIn this paper, we study the moduli space of $2|1$-dimensional complex
associative algebras, which is also the moduli space of codifferentials on the
tensor coalgebra of a $1|2$-dimensional complex space. We construct the moduli
space by considering extensions of lower dimensional algebras. We also
construct miniversal deformations of these algebras. This gives a complete
description of how the moduli space is glued together via jump deformations.Extensions of associative algebras.
Wed, 08/26/2009 - 14:58 — SomNambulAuthors: Alice Fialowski, Michael Penkava
Subjects: Rings and Algebras
AbstractIn this paper, we give a purely cohomological interpretation of the extension
problem for associative algebras; that is the problem of extending an
associative algebra by another associative algebra. We then give a similar
interpretation of infinitesimal deformations of extensions. In particular, we
consider infinitesimal deformations of representations of an associative
algebra.
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