It is well known that a Lie groupoid G canonically defines both a C *-algebra C * (G) and a Poisson manifold A * (G). We show that the maps G → C * (G) and G → A * (G) are functorial with respect to suitably defined categories. The arrows (Hom-spaces) between Lie groupoids are taken to be isomorphism classes of regular bibundles (Hilsum–Skandalis maps), composed by a canonical bibundle tensor p...

In this report we present a brief survey of the existing algorithms for Computing the Automorphism Group of a graph, algorithms to compute Sub Graph Isomorphism(SGI) and also present some important results on Spectrum of a Graph. Graph Isomorphism(GI) has been a great interest of computer scientists the problem of SGI has been proved to be a NP-Complete problem however the complexity class of G...

Abstract We characterize cyclic algebras over the associative and framed little 2-disks operad in any symmetric monoidal bicategory. The cyclicity is appropriately treated a coherent way, that up to isomorphism. When bicategory specified be certain of linear categories subject finiteness conditions, we prove algebras, respectively, are equivalent pivotal Grothendieck–Verdier ribbon categories, ...

Given a variety V of universal algebras. A new approach is suggested to characterize algebraically automorphisms of the category of free V-algebras. It gives in many cases an answer to the problem set by the first of authors, if automorphisms of such a category are inner or not. This question is important for universal algebraic geometry [5, 9]. Most of results will actually be proved to hold f...

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

A self-dual algebra is an associative or Lie algebra A together with an A bimodule isomorphism A → A∨op, where A∨ = Homk(A, k), the dual bimodule to A (considered as an A bimodule), and A∨op is the the same underlying k module as A∨ but is an A bimodule whose left operation by an element a ∈ A is the same as the right operation by a on A∨, and similarly with left and right interchanged. This in...