A Finite Dimensional L∞ Algebra Example in Gauge Theory
ثبت نشده
چکیده
We construct an example of a finite dimensional L∞ algebra which is generated by a Lie algebra together with a non-Lie action on another vector space. We then show how this example fits into the gauge transformation theory of Berends, Burgers and Van Dam.
منابع مشابه
On permutably complemented subalgebras of finite dimensional Lie algebras
Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...
متن کاملKac-Moody Extensions of 3-Algebras and M2-branes
We study the 3-algebraic structure involved in the recently shown M2-branes worldvolume gauge theories. We first extend an arbitrary finite dimensional 3algebra into an infinite dimensional 3-algebra by adding a mode number to each generators. A unique central charge in the algebra of gauge transformations appears naturally in this extension. We present an infinite dimensional extended 3-algebr...
متن کاملساختار فاز میدانهای پیمانهای شبکهای دو بعدی U(N) با کنش مختلط
We study the phase structure of two dimensional pure lattice gauge theory with a Chern term. The symmetry groups are non-Abelian, finite and disconnected sub-groups of SU(3). Since the action is imaginary it introduces a rich phase structure compared to the originally trivial two dimensional pure gauge theory. The Z3 group is the center of these groups and the result shows that if we use one ...
متن کاملA Finite Dimensional A∞ Algebra Example
We construct an example of an A∞ algebra structure defined over a finite dimensional graded vector space. Introduction A∞ algebras (or sha algebras) and L∞ (or sh Lie algebras) have been topics of current research. Construction of small examples of these algebras can play a role in gaining insight into deeper properties of these structures. These examples may prove useful in developing a deform...
متن کاملFrom Large N Matrices to the Noncommutative Torus
We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the C∗-algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of non...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004