Representation Theory for Varieties of Comtrans Algebras and Lie Triple Systems
نویسندگان
چکیده
Comtrans algebras are unital modules over a commutative ring R, equipped with two basic trilinear operations: a commutator [x, y, z] satisfying the left alternative identity [x, x, y] = 0, (1.1) and a translator 〈x, y, z〉 satisfying the Jacobi identity 〈x, y, z〉+ 〈y, z, x〉+ 〈z, x, y〉 = 0, (1.2) such that together the commutator and translator satisfy the comtrans identity [x, y, x] = 〈x, y, x〉. (1.3)
منابع مشابه
Lie-type higher derivations on operator algebras
Motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study Lie-type higher derivations on operator algebras in the current work. It is shown that every Lie (triple-)higher derivation on some classical operator algebras is of standard form. The definition of Lie $n$-higher derivations on operator algebras and related pot...
متن کاملUniversal Central Extension of Current Superalgebras
Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras are very impo...
متن کاملArithmetic Deformation Theory of Lie Algebras
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...
متن کاملDouble derivations of n-Lie algebras
After introducing double derivations of $n$-Lie algebra $L$ we describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual derivation Lie algebra $mathcal Der(L)$. In particular, we prove that the inner derivation algebra $ad(L)$ is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra wit...
متن کاملSuperpotentials for Superconformal Chern–simons Theories from Representation Theory
These notes provide a detailed account of the universal structure of superpotentials defining a large class of superconformal Chern–Simons theories with matter, many of which appear as the low-energy descriptions of multiple M2-brane configurations. The amount of superconformal symmetry in the Chern–Simons-matter theory determines the minimum amount of global symmetry that the associated quarti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IJAC
دوره 21 شماره
صفحات -
تاریخ انتشار 2011