Desingularization in the q-Weyl algebra

Christoph Koutschan; Yi Zhang

doi:10.1016/j.aam.2018.02.005

Desingularization in the q-Weyl algebra

Christoph Koutschan, Yi Zhang^*

^*Corresponding author for this work

Austrian Academy of Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we study the desingularization problem in the first q-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator.

Original language	English
Pages (from-to)	80-101
Number of pages	22
Journal	Advances in Applied Mathematics
Volume	97
DOIs	https://doi.org/10.1016/j.aam.2018.02.005
Publication status	Published - Jun 2018
Externally published	Yes

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Koutschan, C., & Zhang, Y. (2018). Desingularization in the q-Weyl algebra. Advances in Applied Mathematics, 97, 80-101. https://doi.org/10.1016/j.aam.2018.02.005

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abstract = "In this paper, we study the desingularization problem in the first q-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator.",

author = "Christoph Koutschan and Yi Zhang",

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AB - In this paper, we study the desingularization problem in the first q-Weyl algebra. We give an order bound for desingularized operators, and thus derive an algorithm for computing desingularized operators in the first q-Weyl algebra. Moreover, an algorithm is presented for computing a generating set of the first q-Weyl closure of a given q-difference operator. As an application, we certify that several instances of the colored Jones polynomial are Laurent polynomial sequences by computing the corresponding desingularized operator.

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Desingularization in the q-Weyl algebra

Abstract

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