In this paper, three things are done. First, we study from an algebraic point of view the infinite-dimensional Bondi-Metzner-Sachs (BMS)-like extensions Carroll algebra relevant to asymptotic structure electric and magnetic Carrollian limits Einstein gravity. course exhibit by ``Carroll-Galileo duality'' a new BMS-like extension Galilean its centrally extended Bargmann algebra. Second, consider...

A bstract By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that rescaled mode defined by an integral of stress tensor T ++ on 2 plane satisfies Virasoro-like algebra when dimension scalar is large. The structure enhanced to include Kac-Moody-type if ...

The theory of Lie algebras has many applications in mathematics and physics. One possible way of generalizing the theory of Lie algebras is to develop the theory of Lie-like algebras algebras, where the notion of a Lie-like algebras algebra was introduced in [4]. One of Lie’s Theorems claims that the only irreducible representations of a solvable Lie algebra over an algebraically closed field k...

‎let $omega$ be a class of unital‎ ‎$c^*$-algebras‎. ‎we introduce the notion of a local tracial $omega$-algebra‎. ‎let $a$ be an $alpha$-simple unital local tracial $omega$-algebra‎. ‎suppose that $alpha:gto $aut($a$) is an action of a finite group $g$ on $a$‎ ‎which has a certain non-simple tracial rokhlin property‎. ‎then the crossed product algebra‎ ‎$c^*(g,a,alpha)$ is a unital local traci...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

The classical matrix groups are of fundamental importance in many parts of geometry and algebra. Some of them, like Sp.n/, are most conceptually defined as groups of quaternionic matrices. But, the quaternions not being commutative, we must reconsider some aspects of linear algebra. In particular, it is not clear how to define the determinant of a quaternionic matrix. Over the years, many peopl...

The idea that a system obeying interpolating statistics can be described by a deformed oscillator algebra has been an outstanding issue. This original concept introduced long ago by Greenberg is the motivation for this investigation. We establish that a q-deformed algebra can be used to describe the statistics of particles (anyons) interpolating continuously between Bose and Fermi statistics, i...

The free algebra adjunction, between the category of algebras of a monad and the underlying category, induces a comonad on the category of algebras. The coalgebras of this comonad are the topic of study in this paper (following earlier work). It is illustrated how such coalgebras-on-algebras can be understood as bases, decomposing each element x into primitives elements from which x can be reco...

We study a process algebra ATP for the description and analysis of systems of timed processes. An important feature of the algebra is that its vocabulary of actions contains a distinguished element . An occurrence of is a time event representing progress of time. The algebra has, apart from standard operators of process algebras like CCS or ACP, a primitive binary unit-delay operator. For two a...