A-infinity and L-infinity algebra structures arising from (dg) Frobenius algebras (GPS)
Student No.:50
Time:Thu 9:00-10:30, 2017-6-22
Instructor:Zhengfang Wang  [BICMR]
Place:Conference room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-6-22
Ending Date:2017-6-22



Given a (differential graded) Frobenius algebra, one can construct an unbounded complex, called Tate-Hochschild complex, which is defined as a mapping cone of a certain morphism from the Hochschild chain complex (with some shift) to the Hochschild cochain complex. We construct a cyclic (or called Calabi-Yau) A-infinity algebra structure, which extends the classical Hochschild cup and cap products, on the Tate-Hochschild complex. This A-infinity algebra has an explicit formula with m_n=0 for n>3. We will also construct an $L$-infinity algebra structure by extending the classical Gerstenhaber bracket. Moreover, we prove that the cohomology ring of the Tate-Hochschild complex is a Batalin-Vilkovisky (BV) algebra with the BV operator extending the Connes' boundary operator. At the end, we will talk about how to relate the Tate-Hochschild complex to string topology. This talk is based on the recent joint work with M. Rivera.



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