An algebra associated with a subspace lattice over a finite field and its relation to the quantum affine algebra Uq((sl)over-cap2)

JOURNAL OF ALGEBRA

卷:489

Article

Watanabe, Yuta¹ 

[1] Tohoku Univ, Grad Sch Informat Sci, Sendai, Miyagi 9808579, Japan

关键词: Subspace lattice;    Incidence algebra;    Quantum affine algebra;   

DOI  :  10.1016/j.jalgebra.2017.06.033

来源: Elsevier

【 摘 要 】

It is known that the incidence algebra of a subspace lattice over a finite field with q elements is a homomorphic image of the quantum algebra U-q1/2 (sl(2)). In this paper, we extend this situation. For a fixed proper subspace (which is an object of the subspace lattice), we define naturally a new algebra H which contains the incidence algebra as a proper subalgebra, and show how it is related to the quantum affine algebra U-q1/2 ((sl) over cap (2)). We show that there is an algebra homomorphism from U-q1/2 ((sl) over cap (2)) to H, and that H is generated by its image together with the center. Moreover, we show that any irreducible H-module is also irreducible as a U-q1/2 ((sl) over cap (2))-module and is isomorphic to the tensor product of two evaluation modules. We also obtain a small set of generators of the center of H. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free