Quantum Algebra

New submissions

• New submissions
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New submissions for Tue, 14 May 24

[1]  arXiv:2405.06982 [pdf, other]

Title: Quantum groups from homologies of configuration spaces

Authors: Stephen Bigelow, Jules Martel

Comments: 46p. many figures

Subjects: Quantum Algebra (math.QA); Geometric Topology (math.GT)

We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our diagrams represent true submanifolds of configuration spaces and combinatorial relations between them translate actual twisted homological relations.

[2]  arXiv:2405.07126 [pdf, ps, other]

Title: Boundary minimal models and the Rogers-Ramanujan identities

Authors: Diego Salazar

Comments: 24 pages

Subjects: Quantum Algebra (math.QA); Combinatorics (math.CO)

We determine when the irreducible modules $L(c_{p, q}, h_{m, n})$ over the simple Virasoro vertex algebras $\operatorname{Vir}_{p, q}$, where $p, q \ge 2$ are relatively prime with $0 < m < p$ and $0 < n < q$, are classically free. It turns out this only happens with the boundary minimal models, i.e., with the irreducible modules over $\operatorname{Vir}_{2, 2s + 1}$ for $s \in \mathbb{Z}_+$. We thus obtain a complete description of the classical limits of these modules in terms of the jet algebra of the corresponding Zhu $C_2$-algebra. Gordon's generalization of the Rogers-Ramanujan identities is used in the proof, and our results in turn provide a natural interpretation of these identities.

[3]  arXiv:2405.07643 [pdf, ps, other]

Title: Automorphism groups of certain orbifold vertex operator algebras arising from coinvariant lattices associated with the Leech lattice

Authors: Takara Kondo

Comments: arXiv admin note: text overlap with arXiv:2103.08085 by other authors

Subjects: Quantum Algebra (math.QA); Group Theory (math.GR)

We determine the automorphism groups of the orbifold vertex operator algebras associated with the coinvariant lattices of isometries of the Leech lattice in the conjugacy classes 3C, 5C, 11A and 23A. These orbifold vertex operator algebras appear in a classification given by C.H. Lam and H. Shimakura.

[4]  arXiv:2405.07866 [pdf, other]

Title: Complex structures on Three-point space

Authors: Suvrajit Bhattacharjee, Debashish Goswami

Comments: This is an old article written in 2017 and it appeared in print only recently. It forms a short section of the first author's thesis

Subjects: Quantum Algebra (math.QA)

We discuss notions of almost complex, complex and K\"{a}hler structures in the realm of non-commutative geometry and investigate them for a class of finite dimensional spectral triples on the three-point space. We classify all the almost complex structures on this non-commutative manifold, which also turn out to be complex structures, but none of them are K\"{a}hler in our sense.

Replacements for Tue, 14 May 24

[5]  arXiv:2306.00558 (replaced) [pdf, ps, other]

Title: Infinitesimal braidings and pre-Cartier bialgebras

Authors: A. Ardizzoni, L. Bottegoni, A. Sciandra, T. Weber

Comments: 38 pages; conceptualized proof of Prop. 2.7; improved formulations in Def. 2.1, Def. 3.1 and in Thm. 2.6, Thm. 3.2; connection to matched pairs discussed before Lem. 3.16; adjusted relations for $\mathrm{M}_q(2)$ and computations on pages 21-23; minor typo corrections

Subjects: Quantum Algebra (math.QA); Category Theory (math.CT); Rings and Algebras (math.RA); Representation Theory (math.RT)

[6]  arXiv:1906.09362 (replaced) [pdf, other]

Title: Random Finite Noncommutative Geometries and Topological Recursion

Authors: Shahab Azarfar, Masoud Khalkhali

Comments: 44 pages, two references added to the new version, published (online first) Ann. Inst. Henri Poincar\'e Comb. Phys. Interact. (2024)

Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)

[7]  arXiv:2301.11593 (replaced) [pdf, ps, other]

Title: The Donovan--Wemyss Conjecture via the Derived Auslander--Iyama Correspondence

Authors: Gustavo Jasso, Bernhard Keller, Fernando Muro

Comments: 25 pages. v4: Corrected several minor typos. v3: New title; final version; to appear in the proceedings of the Abel Symposium 2022: Triangulated categories in representation theory and beyond

Subjects: Algebraic Geometry (math.AG); Quantum Algebra (math.QA); Representation Theory (math.RT)

[8]  arXiv:2307.00435 (replaced) [pdf, ps, other]

Title: Weakly Parametric Pseudodifferential Calculus for Twisted $C^*$-dynamical Systems

Authors: Gihyun Lee, Matthias Lesch

Comments: v2: additional details in the proof of Theorem 5.2, 28 pages

Subjects: Operator Algebras (math.OA); Functional Analysis (math.FA); Quantum Algebra (math.QA)

[9]  arXiv:2309.15330 (replaced) [pdf, ps, other]

Title: Characters of $GL_n(\mathbb F_q)$ and vertex operators

Authors: Naihuan Jing, Yu Wu

Comments: 24 pages, one chart; Final version

Journal-ref: J. Algebra (2024)

Subjects: Representation Theory (math.RT); Combinatorics (math.CO); Group Theory (math.GR); Quantum Algebra (math.QA)

[10]  arXiv:2405.01513 (replaced) [pdf, ps, other]

Title: Geometric Quantization Without Polarizations

Authors: Joshua Lackman

Comments: 20 pages. Fixed typos, minor edits to exposition and references

Subjects: Symplectic Geometry (math.SG); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA)

[11]  arXiv:2405.04337 (replaced) [pdf, other]

Title: On the Kauffman bracket skein module of $(S^1 \times S^2) \ \# \ (S^1 \times S^2)$

Authors: Rhea Palak Bakshi, Seongjeong Kim, Xiao Wang

Comments: 30 pages, 20 figures

Subjects: Geometric Topology (math.GT); Quantum Algebra (math.QA)

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• Replacements