具有两个单模的泛变形环和二面角块
Universal deformation rings and dihedral blocks with two simple modules
摘要：
设k是特征为2的代数闭域，W是k上的无穷Witt向量环.设G是一个有限群，B是kG的一个块，它具有一个二面体亏群D，使得仅有两个同构类的单B-模.对于B中的任意k-生成kG-模V，确定了其稳定自同态环同构于k的泛变形环R（G，V）.埃德曼对B的基本代数的关系的描述通常只在某个参数c为0或1时才确定。证明了R（G，V）同构于WD的子商环当且仅当c=0，从而回答了第一作者和Chinburg在这种情况下提出的一个问题.此外，我们还证明了c=0当且仅当B是Morita等价于一个主块.
英文摘要：
Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group and B is a block of kG with a dihedral defect group D such that there are precisely two isomorphism classes of simple B-modules. We determine the universal deformation ring R(G,V) for every finitely generated kG-module V which belongs to B and whose stable endomorphism ring is isomorphic to k. The description by Erdmann of the quiver and relations of the basic algebra of B is usually only determined up to a certain parameter c which is either 0 or 1. We show that R(G,V) is isomorphic to a subquotient ring of WD for all V as above if and only if c=0, giving an answer to a question raised by the first author and Chinburg in this case. Moreover, we prove that c=0 if and only if B is Morita equivalent to a principal block.
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