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- W4286962584 abstract "The `spider theorem' for a general Frobenius algebra $A$, classifies all maps $A^{otimes m}to A^{otimes n}$ that are built from the operations and, in a graphical representation, represented by a {it connected} diagram. Here the algebra can be noncommutative and the Frobenius form can be asymmetric. We view this theorem as reducing any connected diagram to a standard form with $j$ beads $B$, where $j$ is the number of bounded connected components of the original diagram. We study the associated F-dimension Hilbert series $dim_x=sum_{j=0}^infty x^jdim_j$, where $dim_j=epsiloncirc B^jcirc 1$ are invariants of the Frobenius structure. We also study moduli of asymmetric quasispecial and `weakly symmetric' Frobenius structures and their F-dimensions. Examples include general Frobenius structures on matrix algebras $A=M_d(k)$ and on group algebras $k G$ as well as on $u_q(sl_2)$ at low roots of unity." @default.
- W4286962584 created "2022-07-25" @default.
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- W4286962584 date "2021-09-24" @default.
- W4286962584 modified "2023-09-26" @default.
- W4286962584 title "Planar spider theorem and asymmetric Frobenius algebras" @default.
- W4286962584 doi "https://doi.org/10.48550/arxiv.2109.12106" @default.
- W4286962584 hasPublicationYear "2021" @default.
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