Quantum Weyl algebras and reflection equation algebras at a root of unity

Noncommutative Algebra and Representation Theory: Symmetry, Structure & Invariants

“…The quantum Weyl algebra and its higher degree analogues are amongst the simplest non-abelian examples of quantum multiplicative quiver varieties (see the recent paper [43]) and have been extensively studied.…”

Dipper Donkin Quantized Matrix Algebra and Reflection Equation Algebra at root of unity

“…([4, Lemma 3.2]) For ≥ 1, the following identities hold in the algebra( 2 ): (i) 12 11 = 11 12 + −2 ( 2 − 1) 12 22 (ii) 21 11 = 11 21 + −2 (1 − 2 ) 22 21 (iii) 21 12 = 12 21 + −2 ( 2 − 1) 11 22 −21 12 = 12 21 + (1 − −2 ) 11 22 −…”