[1]

V. V. Bavula and T. Lu,
Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules,
J. Math. Phys. 58 (2017), no. 1, Article ID 011701.
Web of ScienceGoogle Scholar

[2]

V. V. Bavula and T. Lu,
Classification of simple weight modules over the Schrödinger algebra,
Canad. Math. Bull. 61 (2018), no. 1, 16–39.
CrossrefGoogle Scholar

[3]

Y. Billig,
Jet modules,
Canad. J. Math. 59 (2007), no. 4, 712–729.
CrossrefGoogle Scholar

[4]

Y. Billig and V. Futorny,
Classification of irreducible representations of Lie algebra of vector fields on a torus,
J. Reine Angew. Math. 720 (2016), 199–216.
Web of ScienceGoogle Scholar

[5]

Y. Billig, A. Molev and R. Zhang,
Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus,
Adv. Math. 218 (2008), no. 6, 1972–2004.
CrossrefWeb of ScienceGoogle Scholar

[6]

Y. Billig and J. Talboom,
Classification of category $\mathcal{\mathcal{J}}$ modules for divergence zero vector fields on a torus,
J. Algebra 500 (2018), 498–516.
Google Scholar

[7]

R. E. Block,
The irreducible representations of the Lie algebra $\U0001d530\U0001d529(2)$ and of the Weyl algebra,
Adv. in Math. 39 (1981), no. 1, 69–110.
Google Scholar

[8]

E. Cartan,
Les groupes projectifs qui ne laissent invariante aucune multiplicité plane,
Bull. Soc. Math. France 41 (1913), 53–96.
Google Scholar

[9]

J. Dixmier,
Enveloping Algebras,
North-Holland Math. Libr. 14,
North-Holland, Amsterdam, 1977.
Google Scholar

[10]

S. Eswara Rao,
Irreducible representations of the Lie-algebra of the diffeomorphisms of a *d*-dimensional torus,
J. Algebra 182 (1996), no. 2, 401–421.
CrossrefGoogle Scholar

[11]

S. Eswara Rao,
Partial classification of modules for Lie algebra of diffeomorphisms of *d*-dimensional torus,
J. Math. Phys. 45 (2004), no. 8, 3322–3333.
CrossrefGoogle Scholar

[12]

X. Guo, G. Liu, R. Lu and K. Zhao,
Simple Witt modules that are finitely generated over the Cartan subalgebra,
preprint (2017), https://arxiv.org/abs/1705.03393;
to appear in Mosc. Math. J.

[13]

X. Guo, G. Liu and K. Zhao,
Irreducible Harish-Chandra modules over extended Witt algebras,
Ark. Mat. 52 (2014), no. 1, 99–112.
Web of ScienceCrossrefGoogle Scholar

[14]

X. Guo and K. Zhao,
Irreducible weight modules over Witt algebras,
Proc. Amer. Math. Soc. 139 (2011), no. 7, 2367–2373.
Web of ScienceGoogle Scholar

[15]

N. Jacobson,
Basic Algebra. II,
W. H. Freeman, San Francisco, 1980.
Google Scholar

[16]

T. A. Larsson,
Conformal fields: A class of representations of $\mathrm{Vect}(N)$,
Internat. J. Modern Phys. A 7 (1992), no. 26, 6493–6508.
Google Scholar

[17]

T. A. Larsson,
Lowest-energy representations of non-centrally extended diffeomorphism algebras,
Comm. Math. Phys. 201 (1999), no. 2, 461–470.
CrossrefGoogle Scholar

[18]

T. A. Larsson,
Extended diffeomorphism algebras and trajectories in jet space,
Comm. Math. Phys. 214 (2000), no. 2, 469–491.
CrossrefGoogle Scholar

[19]

G. Liu, R. Lu and K. Zhao,
Irreducible Witt modules from Weyl modules and $\U0001d524{\U0001d529}_{n}$-modules,
J. Algebra 511 (2018), 164–181.
Google Scholar

[20]

G. Liu and K. Zhao,
New irreducible weight modules over Witt algebras with infinite-dimensional weight spaces,
Bull. Lond. Math. Soc. 47 (2015), no. 5, 789–795.
Web of ScienceCrossrefGoogle Scholar

[21]

X. Liu, X. Guo and Z. Wei,
Irreducible modules over the divergence zero algebras and their *q*-analogues,
preprint (2017), https://arxiv.org/abs/1709.02972.

[22]

R. Lü, X. Guo and K. Zhao,
Irreducible modules over the Virasoro algebra,
Doc. Math. 16 (2011), 709–721.
Google Scholar

[23]

R. Lü, V. Mazorchuk and K. Zhao,
Classification of simple weight modules over the 1-spatial ageing algebra,
Algebr. Represent. Theory 18 (2015), no. 2, 381–395.
CrossrefWeb of ScienceGoogle Scholar

[24]

R. Lu and K. Zhao,
Irreducible Virasoro modules from irreducible Weyl modules,
J. Algebra 414 (2014), 271–287.
CrossrefWeb of ScienceGoogle Scholar

[25]

O. Mathieu,
Classification of Harish-Chandra modules over the Virasoro Lie algebra,
Invent. Math. 107 (1992), no. 2, 225–234.
CrossrefGoogle Scholar

[26]

O. Mathieu,
Classification of irreducible weight modules,
Ann. Inst. Fourier (Grenoble) 50 (2000), no. 2, 537–592.
CrossrefGoogle Scholar

[27]

V. Mazorchuk and K. Zhao,
Supports of weight modules over Witt algebras,
Proc. Roy. Soc. Edinburgh Sect. A 141 (2011), no. 1, 155–170.
CrossrefGoogle Scholar

[28]

V. Mazorchuk and K. Zhao,
Characterization of simple highest weight modules,
Canad. Math. Bull. 56 (2013), no. 3, 606–614.
CrossrefGoogle Scholar

[29]

D. K. Nakano,
Projective modules over Lie algebras of Cartan type,
Mem. Amer. Math. Soc. 98 (1992), no. 470.
Google Scholar

[30]

G. Y. Shen,
Graded modules of graded Lie algebras of Cartan type. I. Mixed products of modules,
Sci. Sinica Ser. A 29 (1986), no. 6, 570–581.
Google Scholar

[31]

J. Talboom,
Irreducible modules for the Lie algebra of divergence zero vector fields on a torus,
Comm. Algebra 44 (2016), no. 4, 1795–1808.
CrossrefGoogle Scholar

[32]

H. Tan and K. Zhao,
${\mathcal{\mathcal{W}}}_{n}^{+}$- and ${\mathcal{\mathcal{W}}}_{n}$-module structures on $U({\U0001d525}_{n})$,
J. Algebra 424 (2015), 357–375.
Google Scholar

[33]

H. Tan and K. Zhao,
Irreducible modules over Witt algebras ${\mathcal{\mathcal{W}}}_{n}$ and over $\U0001d530{\U0001d529}_{n+1}(\u2102)$,
Algebr. Represent. Theory 21 (2018), no. 4, 787–806.
Google Scholar

[34]

J. Zhang,
Non-weight representations of Cartan type S Lie algebras,
Comm. Algebra 46 (2018), no. 10, 4243–4264.
CrossrefGoogle Scholar

[35]

K. Zhao,
Weight modules over generalized Witt algebras with 1-dimensional weight spaces,
Forum Math. 16 (2004), no. 5, 725–748.
Google Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.