Module algebra structures of nonstandard quantum group X_q(A₁) on the quantum plane

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Abstract

In this paper, for n ≥ 2 and n ≠ 3, the module algebra structures of X_q(A₁) on the quantum n-space were discussed, where the quantum n-space is denoted by A_q(n). In particular, a complete list of X_q(A₁)-module algebra structures on the quantum plane A_q(2) was produced and the isomorphism classes of these structures were described.

Keywords

nonstandard quantum group / quantum n-space / Hopf action / module algebra / weight

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