Classification of simple linearly compact n-Lie superalgebras

We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras of the form L=\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g, where dim L_{n-1}=1, L_{-1} and L_{n-1} generate L, and [L_j, L_{n-j-1}] =0 for all j, thereby reducing it to the known classification of simple linearly compact Lie superalgebras and their Z-gradings. The list consists of four examples, one of them being the n+1-dimensional vector product n-Lie algebra, and the remaining three infinite-dimensional n-Lie algebras.Comment: Final version to appear in Communications in Mathematical Physic

CALENDAR PLANNING IN THE CLUSTER MANAGEMENT SYSTEM OF ENTERPRISES OF THE AGRO-INDUSTRIAL AND COTTON-TEXTILE COMPLEX

Abstract: The paper examines methodological approaches to drawing up a production plan, regardless of the level and hierarchy of cluster planning. The authors note that plans are not only voluminous, such as long-term, current production plans, but also necessarily operational-calendar, i.e. including the distribution of volumetric indicators in time - according to planned periods, as well as in space - according to cluster technological stages (workshops, sections) of production of an agro-industrial enterprise, and within the enterprise along a single production and technological chain of production