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

这个美国-匈牙利的一个研究项目是由威斯康星州的迈克尔·彭卡瓦和布达佩斯的奥特沃斯·罗兰大学的爱丽丝·菲亚洛夫斯基共同完成的，他们研究了无穷代数的无穷变形。合作建立在Penkava的优势，无穷代数和变形理论和Fialowski的变形李代数。 他们的联合研究计划包括自动计算上同调中的李括号，作为他们研究具有不变内积的李代数的双曲变形的继续。他们预期无穷代数的上同调继承了一个自然的过滤，并且这个过滤可以用来定义一个分次对偶空间，这个空间足够小，可以用来构造一个可变形的空间。相关的工作，这个美国和匈牙利的团队的应用广义梅西产品的计算李代数的minierals变形将得到扩展。结合的工作，预计将提高目前的理解的结构的李代数的不变内积以及图复形的同源性。 如果成功的话，这些结果可能会在物理学中有用，在物理学中，可观测量的代数可以描述物理现实，作为经典物理学交换代数的变形量子化。 这个数学研究项目通过使美国和中欧的专家能够联合收割机互补人才，并在相互感兴趣和有能力的领域共享研究资源，实现了推进科学知识的计划目标。

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.