The nil-blob algebra: An incarnation of type [formula omitted] Soergel calculus and of the truncated blob algebra

Abstract

We introduce a type B analogue of the nil Temperley-Lieb algebra in terms of generators and relations, that we call the (extended) nil-blob algebra. We show that this algebra is isomorphic to the endomorphism algebra of a Bott-Samelson bimodule in type A˜1. We also prove that it is isomorphic to an idempotent truncation of the classical blob algebra.