2024/08/05 by Shivang Jindal, Jindal, Shivang · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2408.02618
openalex publication_date 2024/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate the deformed and non-deformed cohomological Hall algebra (CoHA) of the preprojective algebra for the case of cyclic quivers by studying the Kontsevich-Soibelman CoHA and using tools from cohomological Donaldson-Thomas theory. We show that for the cyclic quiver of length K, this algebra is the universal enveloping algebra of the positive half of a certain extension of matrix differential operators on ℂ*, while its deformation gives a positive half of an explicit integral form of Guay's Affine Yangian Yℏ1,ℏ2(\mathfrakgl(K)). By the main theorem of Botta-Davison (2023) and Schiffmann-Vasserot (2023), we also determine the Maulik-Okounkov Yangian for the case of cyclic quivers. Furthermore, we explain the construction of factorization coproduct, provide evidence for the strong rationality conjecture, calculate the spherical subalgebra of the non-deformed CoHA for any quiver without loops, recover results about the CoHA of compactly supported semistable sheaves on the minimal resolution of the Kleinian singularity ℂ2/ℤK and identify a commutative algebra inside the additive shuffle algebra associated to the cyclic quiver. We end by conjecturally relating the obtained integral form with the algebra defined by Gaiotto-Rapčák-Zhou, in the context of twisted M-theory.