Related papers: Extension of IIB Matrix Model by Three-Algebra
We argue that one can relax the requirements of the non-associative three-algebras recently used in constructing D=3, N=8 superconformal field theories, and introduce the notion of ``relaxed three-algebras''. We present a specific…
In this paper, we introduce the notion of derivations of Lie 2-algebras and construct the associated derivation Lie 3-algebra. We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence…
Over algebraically closed fields of characteristic p>2, prolongations of the simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. Several new simple Lie…
The IIB matrix model proposes a mechanism for dynamically generating four dimensional space--time in string theory by spontaneous breaking of the ten dimensional rotational symmetry $\textrm{SO}(10)$. Calculations using the Gaussian…
The aim of this paper is to generalise the construction of $3$-Bihom-Lie superalgebras and we provide some properties can be lifted to its $T^{\ast}$-extensions such as nilpotency, solvability and decomposition. We study the…
We study the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argue that the large N limit describes the (2,0) Little String Theory. The one-loop effective action shows that the force exerted between two diagonal…
A class of simple filtered Lie algebras of polynomial growth with increasing filtration is distinguished and presentations of these algebras are explicitely described for the simplest examples. Lie (super)algebras of this class appear in…
Recent work applying higher gauge theory to the superstring has indicated the presence of `higher symmetry'. Infinitesimally, this is realized by a `Lie 2-superalgebra' extending the Poincare superalgebra in precisely the dimensions where…
We propose a notion of a super n-Lie algebra and construct a super n-Lie algebra with the help of a given binary super Lie algebra which is equipped with an analog of a supertrace. We apply this approach to the super Lie algebra of a…
We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (super)algebras with indecomposable Cartan matrix, and (under…
We prove a structure theorem for Lie n-algebras possessing an invariant inner product. We define the notion of a double extension of a metric Lie n-algebra by another Lie n-algebra and prove that all metric Lie n-algebras are obtained from…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
A Lie (super)algebra with a non-degenerate invariant symmetric bilinear form $B$ is called a nis-(super)algebra. The double extension $\mathfrak{g}$ of a nis-(super)algebra $\mathfrak{a}$ is the result of simultaneous adding to…
We show that a recently proposed Yang-Mills matrix model with an auxiliary field, which is a candidate for a non-perturbative description of type IIB superstrings, captures the Euler characteristic of moduli space of Riemann surfaces. This…
We consider random superstrings of type IIB in $d$-dimensional space. The discretized action is constructed from the supersymetric matrix model, which has been proposed as a constructive definition of superstring theory. Our action is…
A classification of the semisimple subalgebras of the Lie algebra of traceless $3\times 3$ matrices with complex entries, denoted $A_2$, is well-known. We classify its nonsemisimple subalgebras, thus completing the classification of the…
We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a…
I review the properties of a matrix action of relevance for IIB superstrings. This model generalizes the action proposed by Ishibashi, Kawai, Kitazawa, and Tsuchiya by introducing an auxillary field Y, which is the matrix version of the…
We provide a systematic analysis of three-dimensional N = 2 extended Bargmann superalgebra and its Newton-Hooke, Lifshitz and Schr\"odinger extensions. These algebras admit invariant non-degenerate bi-linear forms which we utilized to…
We study a matrix model describing type IIB superstring in orbifold backgrounds. We particularly consider a {\bf C}^3/{\bf Z}_3 orbifold model whose six dimensional transverse space is orbifolded by {\bf Z}_3 discrete symmetry. This model…