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Original Articles

Free 2-step nilpotent Lie algebras and indecomposable representations

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Pages 2990-3005 | Received 07 Jun 2017, Published online: 15 Dec 2017

References

  • Cagliero, L., Gutiérrez Frez, L., Szechtman, F. (2016). Classification of finite dimensional uniserial representations of conformal Galilei algebras. J. Math. Phys. 57:101706.
  • Cagliero, L., Szechtman, F. (2013). The classification of uniserial 𝔰𝔩(2)⋉V(m)–modules and a new interpretation of the Racah–Wigner 6j–symbol. J. Algebra 386:142–175.
  • Cagliero, L., Szechtman, F. (2014). On the theorem of the primitive element with applications to the representation theory of associative and Lie algebras. Canad. Math. Bull. 57:735–748.
  • Cagliero, L., Szechtman, F. (2016). Indecomposable modules of 2-step solvable Lie algebras in arbitrary characteristic. Commun. Algebra 44:1–10.
  • Casati, P. (2010). Irreducible SLn+1 representations remain indecomposable restricted to some abelian aubalgebras. J. Lie Theory 20:393–407.
  • Casati, P. (2017). The classification of the perfect cyclic 𝔰𝔩(n+1)⋉ℂn+1–modules. J. Algebra 476:311–343.
  • Casati, P., Minniti, S., Salari, V. (2010). Indecomposable representations of the Diamond Lie algebra. J. Math. Phys. 51:033515, 20.
  • Casati, P., Previtali, A., Szechtman, F. (2017). Indecomposable modules of a family of solvable Lie algebras. Linear Algebra Appl. 531:423–446.
  • Douglas, A., de Guise, H. (2010). Some nonunitary, indecomposable representations of the Euclidean algebra 𝔢(3). J. Phys. A Math. Theory 43:085204.
  • Douglas, A., Premat, A. (2007). A class of nonunitary, finite dimensional representations of the euclidean algebra 𝔢(2). Commun. Algebra 35:1433–1448.
  • Douglas, A., Repka, J. (2011). Indecomposable representations of the Euclidean algebra 𝔢(3) from irreducible representations of (4). Bull. Aust. Math. Soc. 83:439–449.
  • Eisenbud, D., Griffith, P. (1971). Serial rings. J. Algebra 17:389–400.
  • Gelfand, I. M., Ponomarev, V. A. (1969). Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space. Functional Anal. Appl. 3:325–326.
  • Jakobsen, H. P. (2011). Indecomposable Finite-Dimensional Representations of a Class of Lie Algebras and Lie Superalgebras, Supersymmetry in Mathematics and Physics, Lecture Notes in Mathematics, 2027. Heidelberg: Springer, pp. 125–138.
  • Makedonskyi, I. (2013). On wild and tame finite-dimensinal Lie algebras. Funct. Anal. Appl. 47:271–283.
  • Nakayama, T. (1941). On Frobeniusean algebras II. Ann. Math. 42:1–21.
  • Piard, A. (1986). Sur des représentations indécomposables de dimension finie de SL(2).R2. J. Geom. Phys. 3:1–53.
  • Repka, J., de Guise, H. (1999). Some finite-dimensional indecomposable representations of E(2). J. Math. Phys. 40:6087–6109.

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