The krull and global dimension of the tensor product of n-dimensional quantum tori

2014/09/23 by Ashish Gupta, Gupta, Ashish
Computer Science · Mathematics · #16T20 #17B37 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Computing Algorithms and Architecture #Rings and Algebras (math.RA) #math.RA #msc:16T20 #msc:17B37 #msc:20G42

paper · pdf · doi:10.48550/arxiv.1409.6434

openalex publication_date 2014/09/23 · arxiv created 2014/11/01 · arxiv updated 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The n-dimensional quantum torus is defined as the F-algebra generated by variables x₁, ⋯, x_n together with their inverses satisfying the relations x_ix_j = q_ijx_jx_i, where q_ij ∈ F. The Krull and global dimensions of this algebra are known to coincide and the common value is equal to the supremum of the rank of certain subgroups of ⟨ x₁, ⋯, x_n ⟩ that can be associated with this algebra. In this paper we study how these dimensions behave with respect to taking tensor products of quantum tori %over the base field. We derive a best possible upper bound for the dimension of such a tensor product and %deduce from this special cases in which the dimension is additive with respect to tensoring.

Citations

• Representations of the quantum torus and applications to finitely presented groups

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