2024/06/11 by Dmitry V. Talalaev, Talalaev, Dmitry V.
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Fuzzy and Soft Set Theory #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2406.07434
openalex publication_date 2024/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1991, Gelfand and Retakh embodied the idea of a noncommutative Dieudonne determinant in the case of RTT algebra, namely, they found a representation of the quantum determinant of RTT algebra in the form of a product of principal quasi-determinants. In this note we construct an analogue of the above statement for the RE-algebra corresponding to the Drinfeld R-matrix for the order n=2,3. Namely, we have found a family of quasi-determinants that are principal with respect to the antidiagonal, commuting among themselves, whose product turns out to be the quantum determinant of this algebra. This family generalizes the construction of integrals of the full Toda system due to Deift et al. for the quantum case of RE-algebras. In our opinion, this result also clarifies the role of RE-algebras as a quantum homogeneous spaces and can be used to construct effective quantum field theories with a boundary.