Swarnava Mukhopadhyay
TIFR, Mumbai
May 29, 2025
Associative algebras from topology: Given a complex vector space $V$ with a non-degenerate bilinear form and a choice of orthonormal basis $\{e_i\}$, we can try to decorate $V$ with the structure of an associative, commutative algebra. The naive approach is by assigning structure constant $\{\Phi_{i,j,k}\}$ for a multiplication $\ast$, namely $e_i\ast e_j=\sum \Phi_{i,j,k}e_k$ such that $\ast$ is commutative and associative. These impose several relations between the structure constants, which we will refer to as associativity constraints. In this talk we will discuss a recipe on how to resolve these associativity constraints using some formalisms from topology. We will focus on one particular example and discuss how the above formalism can be used to solve another question arising in a different context.
TIFR, Mumbai
May 29, 2025
Associative algebras from topology: Given a complex vector space $V$ with a non-degenerate bilinear form and a choice of orthonormal basis $\{e_i\}$, we can try to decorate $V$ with the structure of an associative, commutative algebra. The naive approach is by assigning structure constant $\{\Phi_{i,j,k}\}$ for a multiplication $\ast$, namely $e_i\ast e_j=\sum \Phi_{i,j,k}e_k$ such that $\ast$ is commutative and associative. These impose several relations between the structure constants, which we will refer to as associativity constraints. In this talk we will discuss a recipe on how to resolve these associativity constraints using some formalisms from topology. We will focus on one particular example and discuss how the above formalism can be used to solve another question arising in a different context.