Shuffle algebra realization of quantum affine superalgebra Uv(Dˆ(2,1;θ))

2021 ◽  
Vol 573 ◽  
pp. 539-560
Author(s):  
Boris Feigin ◽  
Yue Hu
Keyword(s):  
Shuffle Algebra ◽  
Quantum Affine Superalgebra

The shuffle Hopf algebra and noncommutative full completeness

1998 ◽  
Vol 63 (4) ◽  
pp. 1413-1436 ◽  
Author(s):  
R. F. Blute ◽  
P. J. Scott
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Linear Logic ◽  
Natural Extension ◽  
Additive Group ◽  
Completeness Theorem ◽  
Vector Spaces ◽  
Invariance Condition ◽  
Shuffle Algebra ◽  
Topological Vector Spaces

AbstractWe present a full completeness theorem for the multiplicative fragment of a variant of noncommutative linear logic, Yetter's cyclic linear logic (CyLL). The semantics is obtained by interpreting proofs as dinatural transformations on a category of topological vector spaces, these transformations being equivariant under certain actions of a noncocommutative Hopf algebra called the shuffle algebra Multiplicative sequents are assigned a vector space of such dinaturals, and we show that this space has as a basis the denotations of cut-free proofs in CyLL + MIX. This can be viewed as a fully faithful representation of a free *-autonomous category, canonically enriched over vector spaces.This paper is a natural extension of the authors' previous work, “Linear Läuchli Semantics”, where a similar theorem is obtained for the commutative logic MLL + MIX. In that paper, we interpret proofs as dinaturals which are invariant under certain actions of the additive group of integers. Here we also present a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras in this paper corresponds to the passage from commutative to noncommutative logic. However, in our noncommutative setting, one must still keep the invariance condition on dinaturals.

scholarly journals Twisted quantum affine superalgebra , invariantR-matrices and a new integrable electronic model

1997 ◽  
Vol 30 (12) ◽  
pp. 4313-4325 ◽  
Author(s):  
Mark D Gould ◽  
Jon R Links ◽  
Yao-Zhong Zhang ◽  
Ioannis Tsohantjis
Keyword(s):  
Electronic Model ◽  
Quantum Affine Superalgebra

scholarly journals On the K-Theoretic Hall Algebra of a Surface

2020 ◽  
Author(s):  
Yu Zhao
Keyword(s):  
Projective Surface ◽  
Hall Algebra ◽  
Shuffle Algebra ◽  
Coherent Sheaves ◽  
Smooth Projective Surface

Abstract In this paper, we define the $K$-theoretic Hall algebra for dimension $0$ coherent sheaves on a smooth projective surface, prove that the algebra is associative, and construct a homomorphism to a shuffle algebra introduced by Negut [ 10].

scholarly journals A Level-One Representation of the Quantum Affine Superalgebra $\UqMN$

1997 ◽  
Vol 188 (2) ◽  
pp. 367-378 ◽  
Author(s):  
Kazuhiro Kimura ◽  
Jun'ichi Shiraishi ◽  
Jun Uchiyama
Keyword(s):  
Quantum Affine Superalgebra
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