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

Format:

Book

Author/Creator:

Khovanov, Mikhail, author.

Qi, You, author.

Sussan, Joshua, author.

Series:

Memoirs of the American Mathematical Society ; v. 1462.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1462

Language:

English

Subjects (All):

Algebra.

algebra.

Physical Description:

v, 94 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, [2024]

Summary:

"We categorify a tensor product of two Weyl modules for quantum sL2 at a prime root of unity." -- Provided by publisher

Contents:

Chapter 1. Introduction ; 1.1. Motivation ; 1.2. Summary of contents ; 1.3. Further comments ; Acknowledgements

Chapter 2. The quantum group at prime roots of unity ; 2.1. The small quantum sl2 ; 2.2. 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. Grothendieck groups

Chapter 4. A double centralizer property ; 4.1. Extension of categorical actions I ; 4.2. Self-injective algebras ; 4.3. Frobenius algebras ; 4.4. Extension of categorical actions II ; 4.5. A p-DG context

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 p-DG 2-category UR

Chapter 6. The nilHecke algebra ; 6.1. Definitions ; 6.2. Idempotents ; 6.3. p-DG structure ; 6.4. A categorification of simples

Chapter 7. Some cyclic modules ; 7.1. Cellular structure ; 7.2. Specht modules ; 7.3. The modules G(λ)

Chapter 8. Two-tensor quiver Schur algebra ; 8.1. Quiver Schur algebra ; 8.2. A category of nilHecke modules ; 8.3. Extension of categorical actions III ; 8.4. A basic algebra ; 8.5. A basis for truncated modules

Chapter 9. p-DG Webster algebras ; 9.1. Definitions ; 9.2. Connection to quiver Schur algebras ; 9.3. Examples

Chapter 10. A categorification of a tensor product ; 10.1. The main theorem ; 10.2. Stratified structure ; 10.3. Future directions

Bibliography.

Notes:

"January 2024, volume 293, number 1462 (sixth of 7 numbers)."

Includes bibliographical references (pages 93-94).

ISBN:

1470468719

9781470468712

OCLC:

1420316431