On One Algebra of Temperley–Lieb Type

نویسنده

  • Nataly POPOVA
چکیده

An algebra generated by projections with relations of Temperley–Lieb type is considered. Knowledge of Gröbner basis of the ideal allows to find a linear basis of the algebra. Some questions of representation theory for this algebra were studied in [13]. Obtained in the present paper are the additional relations, which hold in all finite-dimensional irreducible ∗-representations, although they do not hold in the algebra.

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

Commuting families in Hecke and Temperley-Lieb Algebras

We define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements i...

متن کامل

. R A ] 2 8 A ug 2 00 4 DESCRIPTION OF THE CENTER OF THE AFFINE TEMPERLEY - LIEB ALGEBRA OF TYPE Ã

Construction of the diagrammatic version of the affine Temperley-Lieb algebra of type A N as a subring of matrices over the Laurent polynomials is given. We move towards geometrical understanding of cellular structure of the Temperley-Lieb algebra. We represent its center as a coordinate ring of the certain affine algebraic variety and describe this variety constructing its desingularization.

متن کامل

Virtual Extension of Temperley–lieb Algebra

The virtual knot theory is a new interesting subject in the recent study of low dimensional topology. In this paper, we explore the algebraic structure underlying the virtual braid group and call it the virtual Temperley–Lieb algebra which is an extension of the Temperley–Lieb algebra by adding the group algebra of the symmetrical group. We make a connection clear between the Brauer algebra and...

متن کامل

Temperley–Lieb Words as Valence-Bond Ground States

Based on the Temperley–Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two point correlation functions can be computed employing the Temperley–Lieb relations. Choosing a spin2 representation of the algebra we obtain a generalization o...

متن کامل

Junction Type Representations of the Temperley–Lieb Algebra and Associated Symmetries

Inspired by earlier works on representations of the Temperley–Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of the so called asymmetric twin representation. The underlying symmetry algebra is also examined and it is shown that in addition to certain obvious exact quantum symmetries non trivial quantum algebraic realizations that...

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 2003