Abstract
We propose a simple method for constructing formal deformations of differential graded algebras in the category of minimal A_\infty -algebras. The basis for our approach is provided by the Gerstenhaber algebra structure on A_\infty -cohomology, which we define in terms of the brace operations. As an example, we construct a minimal A_\infty -algebra from the Weyl–Moyal \ast -product algebra of polynomial functions.
Highlights
The concept of homotopy associative algebras, which first appeared in the context of algebraic topology [21], has evolved into a mature algebraic theory with numerous applications in theoretical and mathematical physics [13, 22]
We propose a simple formula for the deformation of families of differential graded algebras (DGA)’s in the category of minimal A∞-algebras
The basis for our construction is provided by a cup product on A∞-cohomology
Summary
The concept of homotopy associative algebras (or A∞-algebras), which first appeared in the context of algebraic topology [21], has evolved into a mature algebraic theory with numerous applications in theoretical and mathematical physics [13, 22]. Given a one-parameter family A = An of DGA’s with differential ∂ : An → An−1, one can define a minimal A∞-algebra deforming the associative product in A in the direction of an (inhomogeneous) Hochschild cocycle ∆ given by any linear combination of One can define the family of graded algebras A = A0 A1, where A0 = A, A1 = M, and the product is given by
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
