Braided cofree Hopf algebras and quantum multi-brace algebras. (Q2898928)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Braided cofree Hopf algebras and quantum multi-brace algebras. |
scientific article; zbMATH DE number 6055143
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Braided cofree Hopf algebras and quantum multi-brace algebras. |
scientific article; zbMATH DE number 6055143 |
Statements
12 July 2012
0 references
quantum multi-brace algebras
0 references
braided algebras
0 references
quantum quasi-shuffle algebras
0 references
tensor spaces
0 references
cotensor algebras
0 references
Hopf bimodules
0 references
Hopf algebras
0 references
quantum groups
0 references
braided cofree coalgebras
0 references
0.9489168
0 references
0.9417621
0 references
0 references
0 references
0 references
0.9235138
0 references
0.9223641
0 references
0.91849697
0 references
Braided cofree Hopf algebras and quantum multi-brace algebras. (English)
0 references
The authors introduce quantum multi-brace algebras in order to quantize algebra structures in a uniform way. Quantum multi-brace algebras generalize \(\mathbb B_\infty\)-algebras as well as braided algebras. For example, every quantum (quasi-)shuffle algebra is a quantum multi-brace algebra. The tensor space of such an algebra admits a braided algebra structure. It is shown that the cotensor algebra over an \(H\)-Hopf bimodule with respect to a Hopf algebra \(H\) is a braided algebra and also a braided coalgebra. This implies that the upper triangular part of a quantum group is a braided algebra.
0 references
