Clifford代数C（1，3）上Dipper-Donkin量子化GL_2的作用
Actions of the Dipper-Donkin quantization GL_2 on the Clifford algebra C(1,3)
摘要：
本文利用已有的研究GL_q（2，C）在Clifford代数C（1，3）上作用及其量子不变量的方法（Commun. in Algebra 27，1843-1878（1999）），研究了Dipper和Donkin构造的量子群GL_2在C（1，3）上的作用.我们能够证明，存在只有两个非等价的情况下，与非平凡的“扰动”的行动。在这两种情况下，不变量的空间都是平凡的。我们还证明了量子群GL_2的每个不可约有限维代数表示q^m \neq 1都是一维的.通过对零“扰动”情形的研究，我们发现非零“扰动”情形是算子代数\Re唯一具有最大可能维数的情形。
英文摘要：
Following the method already developed for studying the actions of GL_q(2,C) on the Clifford algebra C(1,3) and its quantum invariants (Commun. in Algebra 27, 1843-1878(1999)), we study the action on C(1,3) of the quantum group GL_2 constructed by Dipper and Donkin. We are able of proving that there exists only two non-equivalent cases of actions with nontrivial "perturbation". The space of invariants are trivial in both cases. We also prove that each irreducible finite dimensional algebra representation of the quantum group GL_2, q^m\neq 1, is one dimensional. By studying the cases with zero "perturbation" we find that the cases with nonzero "perturbation" are the only ones with maximal possible dimension for the operator algebra \Re.
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