Presentations of Diagram Categories

Authors

  • Mengwei Hu Sichuan University

DOI:

https://doi.org/10.46787/pump.v3i0.2256

Keywords:

rook category; planar rook category; rook-Brauer category; Motzkin category; partition category; monoidal category; diagrammatic algebra

Abstract

We describe the planar rook category, the rook category, the rook-Brauer category, and the Motzkin category in terms of generators and relations. We show that the morphism spaces of these categories have linear bases given by planar rook diagrams, rook diagrams, rook-Brauer diagrams, and Motzkin diagrams.

Author Biography

Mengwei Hu, Sichuan University

Mengwei Hu is a 4th-year undergraduate majoring in Mathematics at Sichuan University, Chengdu, China. Her interests are representation theory and quantum algebra. She is planning to do a Ph.D. upon graduation.

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Published

2019-12-01

How to Cite

Hu, M. (2019). Presentations of Diagram Categories. The PUMP Journal of Undergraduate Research, 3, 1–25. https://doi.org/10.46787/pump.v3i0.2256

Issue

Vol. 3 (2020): PUMP Journal of Undergraduate Research

Section

Articles

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