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 |
Abstract:
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.
For more lectures of GPS seminar, please refer to http://ymsc.tsinghua.edu.cn/sjcontent.asp?id=921