Jet modules for the centerless Virasoro-like algebra

Guo, Xiangqian; Liu, Genqiang

doi:10.1142/s0219498819500026

Cited by 13 publications

(20 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using this and the same argument as that in the proof of [GL,Lemma 3.5], one gets that λ j,j m,n = λ(α ∨ j ) for all j ∈ J and m, n ∈ Z 2 . It retains to consider the case i = j ∈ J. Firstly, one has that…”

Section: 2mentioning

confidence: 69%

See 1 more Smart Citation

Integrable representations for toroidal extended affine Lie algebras

Chen

Tan

2019

Journal of Algebra

View full text Add to dashboard Cite

show abstract

Section: 2mentioning

confidence: 69%

“…From now on, let T be as in Proposition 4.9. We start with the following three lemmas, whose proof are respectively similar to that in [GL,Lemma 3.3,Proposition 3.4,Lemma 3.6] and are omitted. We denote by J = {i = 1, · · · , ℓ | α ∨ i (m) acts injectively on T, ∀ m = 0}.…”

Section: 2mentioning

confidence: 99%

Integrable representations for toroidal extended affine Lie algebras

Chen

Tan

2019

Journal of Algebra

View full text Add to dashboard Cite

show abstract

“…to emphasize the fact unlike [2] where the corresponding results come by earlier works of authors, we need completely different techinque to prove Proposition 3.10. For its proof hinges on results from [15] (Theorem 3.9 in our paper) and [8]. By Propsition 3.10 it follows that M ∼ = M 1 ⊗ A(m) for some space M 1 .…”

Section: Introductionmentioning

confidence: 83%

Integrable modules for twisted toroidal extended affine Lie algebras

2020

View full text Add to dashboard Cite

In this paper we classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras (twisted toroidal EALA, in short) with finite dimensional weight spaces when the finite dimensional center acts non-trivially. Using an automorphism we reduce to the case where K0 acts non-trivially and Ki, 1 ≤ i ≤ n act trivially. Twisted toroidal EALA has natural triangular decomposition and we prove that any irreducible integrable module of it with finite dimensional weight spaces is a highest weight module with respect to the above triangular decomposition. The highest weight space is an irreducible module for the zeroth component of the twisted toroidal EALA.We then describe the highest weight space in detail.MSC: 17B67,17B66 systematically developed the theory of EALAs (see [1,21,24], and references therein). Unlike affine Kac-Moody algebras, EALAs may have infinite dimensional centers. So representation theory of EALA's is still in progress.Let L ( • INTEGRABLE MODULES FOR TWISTED TOROIDAL EXTENDED AFFINE LIE ALGEBRAS 3 finite order automorphisms σ 0 , . . . , σ n of • g and consider the multi-loop alge-We assume that multi-loop algebra is a Lie torus (see Section 2 for definition). This is not a very serious assumption as it is well known that centerless cores of almost all EALAs are Lie tori [1].We then consider universal central extension of multi-loop algebra and add S n+1 the Lie algebra consisting of divergence zero vector fields on A n+1 (see Section 2 for details). The resulting Lie algebra is EALA called as twised toroidal EALA, and we denote it by T . The aim of this paper is to classify all irreducible integrable representation of twisted toroidal EALAs with finite dimensional weight spaces where center acts non-trivially. The proof of our classification problem runs parallel to [2] where they consider full twisted TLA. Our twisted toroidal EALA is a proper subalgebra of full twisted EALA. Since we working with smaller algebra some of the results used in [2] won't work here. So we use differnt techniques; notably results from [5] and [15] are very special for divergence zero vector fields.We now explain our plan of classification result in more detail. In Section 2 we start with basic definitions which leads up to the definition of twisted toroidal EALA T . In Section 3 we define root space decomposition and using it define a natural triangular decomposition T = T − ⊕ T 0 ⊕ T + . We fix an irreducible integrable module V of T with finite dimensional weight spaces where K 0 acts non-trivially and K i act trivially for 1 ≤ i ≤ n. This assumption is due to the fact that group GL(n + 1, Z) acts as automorphism on FTLA and leaves τ div invariant. Then using earlier work of [2] it follows that the space M = {v ∈ V |T + v = 0} is a non-zero T 0 irreducible module.The rest of the paper revolves around M as we try to decode the structure of

show abstract

“…In this paper we will classify irreducible integrable modules with finite dimensional weight spaces for τ , where the zero degree central operators act trivially for any n ≥ 3. We make use of some important results from [11] and [12] in order to classify our modules.…”

Section: Introductionmentioning

confidence: 99%

“…The idea of the proof of following two lemma is from [12], but the calculations will be tottaly different. So we will give the proofs.…”

mentioning

confidence: 99%

Classification of irreducible integrable modules for extended affine Lie algebras with center acting trivially

Tantubay,

Batra

2021

Preprint

View full text Add to dashboard Cite

show abstract

Jet modules for the centerless Virasoro-like algebra

Cited by 13 publications

References 32 publications

Integrable representations for toroidal extended affine Lie algebras

Integrable representations for toroidal extended affine Lie algebras

Integrable modules for twisted toroidal extended affine Lie algebras

Classification of irreducible integrable modules for extended affine Lie algebras with center acting trivially

Contact Info

Product

Resources

About