This paper gives a way to renormalise certain quantum field theories on compact manifolds. Examples include Yang-Mills theory (in dimension 4 only), Chern-Simons theory and holomorphic Chern-Simons theory. The method is within the framework of the Batalin-Vilkovisky formalism. Chern-Simons theory is renormalised in a way respecting all symmetries (up to homotopy). This yields an invariant of sm...

we introduce a new solution for kawahara-kdv equations. the lie group analysis is used to carry out the integration of this equations. the similarity reductions and exact solutions are obtained based on the optimal system method.

The Bagger–Lambert construction of N = 8 superconformal field theories (SCFT) in three dimensions is based on 3-algebras. Three groups of researchers recently realized that an arbitrary semisimple Lie algebra can be incorporated by using a suitable Lorentzian signature 3-algebra. The SU(N) case is a candidate for the SCFT describing coincident M2-branes. However, these theories contain ghost de...

We study the Killing vectors of quantum ground-state manifold a parameter-dependent Hamiltonian. find that may have symmetries are not visible at level Hamiltonian and different phases matter exhibit symmetries. propose Bianchi-based classification various manifolds using Lie algebra vector fields. Moreover, we explain how to exploit these geodesics explore their behaviour when crossing critica...

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all hidden symmetries generated by in dimensions. show that bilinears produce special Killing–Yano forms conformal forms. After defining Lie algebra structure spinors, we construct operators as generalizations derivative spinor fields. All these constructions together constitute general...

‎let $l$ be a lie algebra‎, ‎$mathrm{der}(l)$ be the set of all derivations of $l$ and $mathrm{der}_c(l)$ denote the set of all derivations $alphainmathrm{der}(l)$ for which $alpha(x)in [x,l]:={[x,y]vert yin l}$ for all $xin l$‎. ‎we obtain an upper bound for dimension of $mathrm{der}_c(l)$ of the finite dimensional nilpotent lie algebra $l$ over algebraically closed fields‎. ‎also‎, ‎we classi...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...