Linearization of W algebras and W superalgebras

نویسنده

  • E. Ragoucy
چکیده

In a recent paper, the authors have shown that the secondary reduction of W-algebras provides a natural framework for the linearization of W-algebras. In particular, it allows in a very simple way the calculation of the linear algebra W(G, H) ≥0 associated to a wide class of W(G,H) algebras, as well as the expression of the W generators of W(G,H) in terms of the generators of W(G, H) ≥0. In this paper, we present the extension of the above technique to W-superalgebras, i.e. W-algebras containing fermions and bosons of arbitrary (positive) spins. To be self-contained the paper recall the linearization of W-algebras. We include also examples such as the linearization of W n algebras; W(sℓ(3|1), sℓ(3)) and W(osp(1|4), sp(4)) ≡ WB 2 superalgebras.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weighted Convolution Measure Algebras Characterized by Convolution Algebras

The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.

متن کامل

Secondary Quantum Hamiltonian Reductions

Recently, it has been shown how to perform the quantum hamiltonian reduction in the case of general sl(2) embeddings into Lie (super)algebras, and in the case of general osp(1|2) embeddings into Lie superalgebras. In another development it has been shown that when H and H are both subalgebras of a Lie algebra G with H ⊂ H, then classically the W(G,H) algebra can be obtained by performing a seco...

متن کامل

Whitney algebras and Letterplace superalgebras

I’ll give an outline of the theory of Whitney algebras of a matroid, with the notions of geometric product and the excahnge relations, I’ll give the letterplace superalgebra coding of these algebras, and I’ll show how this coding allows to get the exchange relations directly from the superstraightening laws. I’ll not speak about the Lax Hopf algebra structure of Whitney algebras. All this is pa...

متن کامل

Universal 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 کامل

On good Z-gradings of basic Lie superalgebras

We discuss the classification of good Z-gradings of basic Lie superalgebras. This problem arose in connection to W -algebras, where good Z-gradings play a role in their construction.

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1995