Searcharxiv⌕ Search

arXiv subjects

Yusuke Arike

Publications and source records attributed to Yusuke Arike.

8 recordsLinked to original sources
arXiv2011

Some remarks on pseudo-trace functions for orbifold models associated with symplectic fermions

We give a method to construct pseudo-trace functions for vertex operator algebras satisfying Zhu's finiteness condition not through higher Zhu's algebras and apply our method to the Z_2-orbifold model associated with d-pairs of symplectic fermions. For d=1, we determine the dimension of the space of one-point functions. For d>1, we construct 2^{2d-1}+3 linearly independent one-point functions and study their values at the vacuum vector.

math.QA↗
arXiv2010

A matrix realization of the quantum group g_{p, q}

In this paper we will find a matrix realizations of the quantum group g_{p, q}. For this purpose, we construct all primitive idempotents and a basis of g_{p, q}. We determine the action of elements of the basis on the indecomposable projective modules, which give rise to a matrix realization of g_{p, q}. By using this result, we obtain a basis of the space of symmetric linear functions on g_{p, q}} and express the symmetric linear functions obtained by the left integral, the balancing element and the center of g_{p, q} in term of this basis.

math.QA↗
arXiv2010

Some remarks on symmetric linear functions and pseudotrace maps

Let A be a finite-dimensional associative algebra and $ϕ$ a symmetric linear function on $A$. In this note, we will show that the pseudotrace maps are obtained as special cases of well-known symmetric linear functions on the endomorphism rings of projective modules. We also prove that modules are interlocked with $ϕ$ if and only if they are projective. As an application of our approach, we will give proofs of several propositions and theorems for pseudotrace maps for an arbitrary finite-dimensional associative algebra.

math.RA↗
arXiv2008

A construction of symmetric linear functions of the restricted quantum group \overline{U}_q (sl_2)

In this paper we construct all the primitive idempotents of the restricted quantum group $\overline{U}_q (sl_2)$ and also determine the multiplication rules among a basis given by the action of generators of $\bar{U}_q (sl_2)$ to the idempotents. By using this result we construct a basis of the space of symmetric linear functions of $\overline{U}_q (sl_2)$ and determine the decomposition of the integral of the dual of $\overline{U}_q (sl_2)$ twisted by the balancing element to the basis of the space of symmetric linear functions.

math.QA↗