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8th Croatian Mathematical Congress

2–5 Jul 2024
Osijek
Europe/Zagreb timezone

Conference office

Session

Algebra

ALG
2 Jul 2024, 16:05
D8 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

D8

School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek

Trg Ljudevita Gaja 6, Osijek

Conveners

Algebra

  • Slaven Kozic

Algebra

  • Ivana Vukorepa

Presentation materials

There are no materials yet.

  1. 61. Linear independence for $C_\ell^{(1)}$ by using $C_{2\ell}^{(1)}$
    Goran Trupčević (University of Zagreb Faculty of Teacher Education)
    02/07/2024, 16:05
    ALG: Algebra
    Talk

    M.Primc and T.Šikić have described a combinatorial spanning set for a standard module for the affine Lie algebra of the type $C_\ell^{(1)}$ and have conjectured that this set is linearly independent. We will prove linear independence for certain classes of these modules by establishing a connection with combinatorial bases of Feigin-Stoyanovsky's type subspace of standard modules for the...

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  2. 91. On the double Yangian of the Lie superalgebra $\mathfrak{gl}_{m|n}$
    Lucia Bagnoli
    02/07/2024, 16:25
    ALG: Algebra
    Talk

    We present some results on the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. We establish the Poincaré-Birkhoff-Witt Theorem for the double Yangian. Then, we construct the dual counterpart of the quantum contraction for the dual Yangian and we show that its coefficients are central elements. As an application, we introduce reflection algebras, certain left coideal...

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  3. 77. W-algebras and their hidden relations
    Shigenori Nakatsuka (University of Alberta)
    02/07/2024, 16:45
    ALG: Algebra
    Talk

    We consider W-algebras, a class of vertex algebras that non-linearly generalize the affine Kac-Moody Lie algebras and the Virasoro Lie algebra. They are obtained from the affine Kac-Moody Lie algebras through quantum Hamiltonian reductions parameterized nilpotent orbits. In this talk, we discuss how W-algebras are related to each other, which is partially anticipated from their connections to...

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  4. 112. Deforming quantum vertex algebra modules by braidings
    Prof. Slaven Kozic (Department of Mathematics, University of Zagreb)
    02/07/2024, 17:05
    ALG: Algebra
    Talk

    In this talk, we will discuss a concept of deformation of quantum vertex algebra module by braiding. Furthermore, we will present its applications to Yangians, their generalizations and reflection algebras. This is a joint work with Lucia Bagnoli.

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  5. 110. Takiff vertex algebra of type $A_1^{(1)}$
    Iva Ćuže (University of Mostar Faculty of Science and Education)
    02/07/2024, 17:30
    ALG: Algebra
    Talk

    In 1971., Steven J. Takiff, while studying invariant polynomial rings, defined a specific extension of the finite-dimensional Lie algebra. In his honor, mathematicians call the corresponding extensions of finite-dimensional simple Lie algebras, but also of some infinite-dimensional Lie algebras, Takiff algebras. Takiff algebras are also known as truncated current Lie algebras or *polynomial...

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  6. 98. Classification of irreducible modules for the affine vertex algebra $L_{-\frac{2n+1}{2}}(\mathfrak{sl}_{2n})$ in certain categories
    Ivana Vukorepa
    02/07/2024, 17:50
    ALG: Algebra
    Talk

    We investigate the representation theory of simple affine vertex algebra $L_k(\mathfrak{g})$ at special non-admissible levels $k_n=-\frac{2n+1}{2}$ for $\mathfrak{g} = \mathfrak{sl}_{2n}$. We classify irreducible $L_{k_n}(\mathfrak{sl}_{2n})$-modules in category $KL_{k_n}(\mathfrak{sl}_{2n})$ and prove that $KL_{k_n}(\mathfrak{sl}_{2n})$ is a semi-simple, rigid braided tensor category.
    In...

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