论文标题
接通性和晦涩的$ n $ -ary代数的会员变形
Membership deformation of commutativity and obscure $n$-ary algebras
论文作者
论文摘要
提出了在代数中“打破”通勤性的一般机制：如果将基本集合视为清晰的集合，而是一个晦涩/模糊的集合，则可以将构件函数（反映出一个元素属于该集合的真理程度）纳入通勤关系中。引入了交换性的特殊“变形”和$ \ varepsilon $ - 交流性的方式，以至于相等的真实程度导致“非事态形式”的情况。我们还素描如何“变形” $ \ VAREPSILON $ -LIE代数和Weyl代数。此外，对上述构造扩展到了$ n $ ar的代数，研究了投影表示形式和$ \ varepsilon $ - 同时性。
A general mechanism for "breaking" commutativity in algebras is proposed: if the underlying set is taken to be not a crisp set, but rather an obscure/fuzzy set, the membership function, reflecting the degree of truth that an element belongs to the set, can be incorporated into the commutation relations. The special "deformations" of commutativity and $\varepsilon $-commutativity are introduced in such a way that equal degrees of truth result in the "nondeformed" case. We also sketch how to "deform" $\varepsilon$-Lie algebras and Weyl algebras. Further, the above constructions are extended to $n$-ary algebras for which the projective representations and $\varepsilon $-commutativity are studied.
