Universität zu Köln

Barmeier, Severin ORCID: 0000-0002-3779-2828 and Wang, Zhengfang (2026). A∞ deformations of extended Khovanov arc algebras and Stroppel's conjecture. Advances in Mathematics, 485. pp. 1-63. Elsevier. ISSN 0001-8708

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Abstract

[Artikel-Nr.: 110733] Extended Khovanov arc algebras Kn m are graded associative algebras which naturally appear in a variety of contexts, from knot and link homology, low-dimensional topology and topological quantum field theory to representation theory and symplectic geometry. C. Stroppel conjectured in her ICM 2010 address that the bigraded Hochschild cohomology groups of Kn m vanish in a certain range, implying that the algebras Kn m admit no nontrivial A∞ deformations, in particular that the algebras are intrinsically formal. Whereas Stroppel’s conjecture is known to hold for the algebras K1 m and Kn 1 by work of Seidel and Thomas, we show that Kn m does in fact admit nontrivial A∞ deformations with nonvanishing higher products for all m, n ≥ 2. We describe both the extended Khovanov arc algebras Kn m and their Koszul duals concretely as path algebras of quivers with relations. This allows us to give an explicit algebraic construction of A∞ deformations of Kn m by using the correspondence between A∞ deformations of a Koszul algebra and filtered associative deformations of its Koszul dual.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Barmeier, Severin UNSPECIFIED https://orcid.org/0000-0002-3779-2828 UNSPECIFIED Wang, Zhengfang UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-812455
Identification Number:	10.1016/j.aim.2025.110733
Journal or Publication Title:	Advances in Mathematics
Volume:	485
Page Range:	pp. 1-63
Number of Pages:	63
Date:	February 2026
Publisher:	Elsevier
ISSN:	0001-8708
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Extended Khovanov arc algebras ; Koszul duality ; A∞ deformations ; Reduction systems ; Kazhdan–Lusztig polynomials English
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/81245