Derivations And Automorphisms Of The Quantum Polynomial Algebra Over An Integral Domain

Let R be an Integral domain, n be an integer greater than 1 and Q = (qij)∈Mn(R)be an n×n matrix whose entries satisfy relations qii = qijqji = 1. Let AQ = AQ[x1,···,xn]be the associative R-algebra with a unit element generated by x1,x2,···,xn, subject todefining relations xixj = qijxjxi. The algebra AQ is called a quantum polynomial algebra.The aims of this paper is (1) to determine the derivation algebra of AQ; (2) to determinethe automorphism group of AQ when qij = q = 1,1≤i < j≤n and for n≥3, q is not aroot of unity.Alev and Chamarie determined the derivation algebra of AQ for a field R and theautomorphism group of AQ for a field R of characteristic 0 when qij = q = 1,1≤i < j≤nand for n≥3, q is not a root of unity. So this paper generalizes their results.