TY  - BOOK
AU  - Goodearl,K.R.
AU  - Yakimov,M.T.
TI  - Quantum cluster algebra structures on quantum nilpotent algebras
T2  - Memoirs of the American Mathematical Society
SN  - 9781470436940 (alk. paper)
U1  - 510 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Quantum groups
KW  - Algebra
N1  - Includes bibliographical references and index; 1. Introduction --
2. Quantum cluster algebras --
3. Iterated skew polynomial algebras and noncommutative UFDs --
4. One-step mutations in CGL extensions --
5. Homogeneous prime elements for subalgebras of symmetric CGL extensions --
6. Chains of mutations in symmetric CGL extensions --
7. Division properties of mutations between CGL extension presentations --
8. Symmetric CGL extensions and quantum cluster algebras --
9. Quantum groups and quantum Schubert cell algebras --
10. Quantum cluster algebra structures on quantum Schubert cell algebras --
Bibliography --
Index
N2  - All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras
ER  -