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Quantum cluster algebra structures on quantum nilpotent algebras / K.R. Goodearl and M.T. Yakimov.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 247, no 1169.Publication details: Providence : American Mathematical Society, 2017.Description: vii, 119 pages ; 26 cmISBN:
  • 9781470436940 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
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.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 138211
Total holds: 0

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.

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.

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