In mathematics, the braid group on n strands (denoted ), also known as the Artin braid group, [1] is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), …

A braid algebra can be: A Gerstenhaber algebra (also called an antibracket algebra). An algebra related to the braid group

Mar 26, 2023 · The branch of topology and algebra concerned with braids, the groups formed by their equivalence classes and various generalizations of these groups [1].

braid is given by an equivalence class of such strands. Together these braids form a group under concatenation, with the identity given by the braid with no twists, and inverse elements given …

2. Geometric Braids The theory of braids begins with a very intuitive geometrical descrip-tion of the main objects of study. De nition 2.1 A geometric braid on nstrings is a subset ˆR2 [0;1] …

1.1 The (pure) braid group via braid diagrams Our first definition of the braid group is as a group of geometric braid diagrams. Informally, a braid on nstrands is (an equivalence class of) …

Apr 30, 2025 · The operations and on strings define a group known as the braid group or Artin braid group, denoted . Topological equivalence for different representations of a braid word …

For nice enough Q, the cluster variety X is a smooth a ne algebraic variety. Moreover, the mixed Hodge structure on the cohomology H (X; Q) is of mixed Tate type, and it is split over Q (in …

groups. Furthermore, the study of these braid groups is also both important to mathematics and applicable to physics. This paper explores the topic of braid groups and braids. The braid …

The braid group on n-strands, denoted B n, is a fundamental algebraic object that has connections to many areas of math including topology, knot theory, and representation theory. …