p-DG cyclotomic nilHecke algebras II / by You Qi, Joshua Sussan.

Format:

Book

Author/Creator:

Qi, You, author.

Sussan, Joshua, author.

Series:

Memoirs of the American Mathematical Society ; v. 1463.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1463

Language:

English

Subjects (All):

Algebra.

algebra.

Physical Description:

v, 106 pages : illustrations ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, [2024]

Summary:

"We categorify tensor products of the fundamental representation of quantum sl2 at prime roots of unity, building upon earlier work where a tensor product of two Weyl modules was categorified." -- Provided by publisher

Contents:

Chapter 1. Introduction ; 1.1. Background ; 1.2. Summary ; 1.3. Organization ; Acknowledgements

Chapter 2. The quantum group sl2 at a root of unity ; 2.1. The small quantum group sl2 ; The BLM integral form ; 2.3. Representations

Chapter 3. Elements of hopfological algebra ; 3.1. p-DG derived categories ; 3.2. Hopfological properties of p-DG modules ; 3.3. p-DG functors ; 3.4. Compact objects and Grothendieck groups ; 3.5. A double centralizer property

Chapter 4. Cellular algebras under p-differential ; 4.1. Graded cellular algebras ; 4.2. p-DG cellular algebras ; 4.3. Quasi-hereditary p-DG cellular algebras ; 4.4. Stratifying derived categories

Chapter 5. A categorification of quantum sl2 at prime roots of unity ; 5.1. The p-DG 2-category U ; 5.2. Thick calculus with the differential ; 5.3. The nilHecke algebra ; 5.4. A categorification of simples

Chapter 6. Some cyclic modules ; 6.1. Cellular combinatorics ; 6.2. Cellular structure on nilHecke algebras ; 6.3. Specht modules ; 6.4. The modules G(λ)

Chapter 7. The quiver Schur algebra ; 7.1. Definition and properties ; 7.2. p-DG cellular structure ; 7.3. The p-DG envelope of cyclic modules ; 7.4. Functors E and F ; 7.5. A comparison of functors

Chapter 8. Webster algebras ; 8.1. Definitions ; 8.2. Diagrammatic quiver Schur algebras ; 8.3. A p-DG Morita equivalence ; 8.4. A diagrammatic cellular basis ; 8.5. p-DG structure on standard modules

Appendix A. Example: the algebra S42 ; A.1. The cellular combinatorics ; A.2. Cyclic nilHecke modules ; A.3. Cellular p-DG modules ; A.4. A basic p-DG algebra

Bibliography

Notes:

"January 2024, volume 293, number 1463 (seventh of 7 numbers)."

Includes bibliographical references (pages 105-106).

ISBN:

1470468727

9781470468729

OCLC:

1420304459