We study completely positive module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions. extend several well known dilation and extension results to this setup, including the Stinespring theorem Wittstock, Arveson, Voiculescu theorems.

We use a fermionic extension of the bosonic module to obtain a class of B(0, N)-graded Lie superalgebras with nontrivial central extensions. 0 Introduction B(M − 1, N)-graded Lie superalgebras were first investigated and classified up to central extension by Benkart-Elduque (see also Garcia-Neher’s work in [GN]). Those root graded Lie superalgebras are a super-analog of root graded Lie algebras...

We begin the study of simple finite-dimensional prime representations of quantum affine algebras from a homological perspective. Namely, we explore the relation between self extensions of simple representations and the property of being prime. We show that every nontrivial simple module has a nontrivial self extension. Conversely, if a simple representation has a unique nontrivial self extensio...

This paper proposes an extension of an SOM called the “SOM of SOMs,” or SOM, in which objects to be mapped are self-organizing maps. In SOM, each nodal unit of a conventional SOM is replaced by a function module of SOM. Therefore, SOM can be regarded as a variation of a modular network SOM (mnSOM). Since each child SOM module in SOM is trained to represent an individual map, the parent map in S...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

We give a natural extension of the notion of the contragredient module for a vertex operator algebra. By using this extension we prove that for regular vertex operator algebras, Zhu’s C2-finiteness condition holds, fusion rules (for any three irreducible modules) are finite and the vertex operator algebras themselves are finitely generated.

1 Divided Power Algebra—October 31, 2016 1 1.1 Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Extension of Divided Power Structure . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Compatible Divided Power structure . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Divided Power Algebra Associated to a Module . . . . . . . . . . . . . . . . . 5 1.5...

With the rapid development of internet technology and protected cultivation in China, it is impending to implement a web-based information service system to spread professional agricultural knowledge. In this study, a 3-layer architecture web-based information service platform (ISP) for protected crop pests was developed using HTML, JavaScript and active server page (ASP). The platform included...

Let p ≥ 3 be a prime. We consider the cyclotomic extension Z(p)[ζp2] of Z(p), with Galois group G := (Z/p2)∗. Since this extension is wildly ramified, Z(p)[ζp2] is not projective as a module over the group ring Z(p)G (Speiser). Extending this module structure, we can regard Z(p)[ζp2 ] as a module over the twisted group ring Z(p)[ζp2] ≀G; as such, it remains faithful and non projective. We calcu...