Quantized matrix algebras and quantum seeds

Abstract

We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees.

Keywords:

• quantized coordinate algebra
• quantum cluster algebra
• quantum seed
• degree and block diagonal form

AMSSubject Classifications:

• Primary: 17B37
• 20G42
• Secondary: 13F60
• 16W35

Notes

The work of C.P is supported by the National Research Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission [grant number FP7-COFUND].