On the N-ary Algebras and Their Universal Covers
نویسنده
چکیده
For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. We discuss the properties of the construction and two simple examples. 1991 Mathematics Subject Classification: 17A42, 16Y99, 17A40
منابع مشابه
On the n-ary algebras, semigroups and their universal
For any n-ary associative algebra we construct a Zn−1 graded algebra, which is a universal object containing the n-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups. AMS Classification: 17A42, 16N34, 20N15
متن کاملIntuitionistic fuzzy n-ary systems
We introduce the basic concepts on intuitionistic fuzzy subalgebras on n-ary groupoids, i.e., on algebras containing one fundamental n-ary operation. We describe some similarities and differences between the n-ary and binary case. In the case of n-ary quasigroups and groups we suggest the common method of investigations based on some methods used in the universal algebra.
متن کاملCharacterization of Protomodular Varieties of Universal Algebras
Protomodular categories were introduced by the first author more than ten years ago. We show that a variety V of universal algebras is protomodular if and only if it has 0-ary terms e1, . . . , en, binary terms t1, . . . , tn, and (n+1)-ary term t satisfying the identities t(x, t1(x, y), . . . , tn(x, y)) = y and ti(x, x) = ei for each i = 1, . . . , n.
متن کاملApplication of fundamental relations on n-ary polygroups
The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...
متن کاملUniversal Central Extension of Current Superalgebras
Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras are very impo...
متن کامل