TL;DR
This paper introduces a new shuffle algebra presentation for the 'top' and 'bottom' halves of the quantum toroidal algebra, leading to a novel topological coproduct extending the Drinfeld-Jimbo coproduct.
Contribution
It provides an orthogonal shuffle algebra framework for quantum toroidal algebra halves, starting from evaluation representations and R-matrices, and defines a new coproduct.
Findings
New shuffle algebra presentations for 'top' and 'bottom' halves
Construction of a topological coproduct extending known structures
Enhanced understanding of quantum toroidal algebra structure
Abstract
As a quantum affinization, the quantum toroidal algebra is defined in terms of its "left" and "right" halves, which both admit shuffle algebra presentations. In the present paper, we take an orthogonal viewpoint, and give shuffle algebra presentations for the "top" and "bottom" halves instead, starting from the evaluation representation of the quantum affine group and its usual R-matrix. An upshot of this construction is a new topological coproduct on the quantum toroidal algebra which extends the Drinfeld-Jimbo coproduct on the horizontal quantum affine subalgebra.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Quantum Information and Cryptography · Quantum Computing Algorithms and Architecture