U.S.-Hungary Mathematics Research on Cohomology and Deformations of Infinity and Lie Algebras

University Of Wisconsin-Eau Claire, Eau Claire WI

Investigators

Abstract

This U.S.-Hungary research project between Michael Penkava of the University of Wisconsin, Eau Claire, and Alice Fialowski of Eotvos Lorand University, Budapest, features versal deformations of infinity algebras. The collaboration builds upon Penkava's strengths in infinity algebras and deformation theory and Fialowski's in deformation of Lie algebras. A qualified undergraduate from the U.S. institution will participate. Their joint research plan entails automated computing of the Lie brackets in the cohomology as a continuation of their study of versal deformations of Lie algebras equipped with an invariant inner product. They anticipate that the cohomology of the infinity algebra inherits a natural filtration and that this filtration can be used to give a definition of a graded dual space which is small enough to be useful in the construction of the versal deformation. Related work by this US-Hungarian team on application of generalized Massey products to computations of miniversal deformations of Lie algebras will be extended as well. The combined work is expected to improve current understanding of the structure of versal deformations of Lie algebras with invariant inner products as well as the homology of the graph complex. If successful, the results may be useful in physics where the algebra of observables can describe physical reality, as a deformation quantization of the commutative algebra of classical physics. This mathematical research project fulfills the program objective of advancing scientific knowledge by enabling experts in the United States and Central Europe to combine complementary talents and share research resources in areas of strong mutual interest and competence.