仿费米子代数及其模和上同调
Parafermionic algebras, their modules and cohomologies
摘要：
本文研究了H.S.共享的每个仿费米子Fock空间允许由仿费米子创建算子的分次2步幂零子代数的分次模的自由最小分解。这样的一个自由决议的帮助下，一个经典的Kostant定理计算李代数上同调的幂零子代数的仿费米Fock空间的值。仿费米Fock空间自由分解的Euler-Poincaré特征给出了Schur多项式之间的一些有趣的恒等式。最后，我们简要地评论了parabosonic和一般parastatistics Fock空间。
英文摘要：
We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded 2-step nilpotent subalgebra of the parafermionic creation operators. Such a free resolution is constructed with the help of a classical Kostant's theorem computing Lie algebra cohomologies of the nilpotent subalgebra with values in the parafermionic Fock space. The Euler-Poincaré characteristics of the parafermionic Fock space free resolution yields some interesting identities between Schur polynomials. Finally we briefly comment on parabosonic and general parastatistics Fock spaces.
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