On the representation type of Jordan basic algebras
Algebra and discrete mathematics, Tome 23 (2017) no. 1, pp. 47-61.

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A finite dimensional Jordan algebra $J$ over a field $\mathbf{k}$ is called basic if the quotient algebra $J/\operatorname{Rad} J$ is isomorphic to a direct sum of copies of $\mathbf{k}$. We describe all basic Jordan algebras $J$ with $(\operatorname{Rad} J)^2=0$ of finite and tame representation type over an algebraically closed field of characteristic 0.
Keywords: Jordan algebra, representation type, quiver of an algebra.
Mots-clés : Jordan bimodule
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Iryna Kashuba; Serge Ovsienko; Ivan Shestakov. On the representation type of Jordan basic algebras. Algebra and discrete mathematics, Tome 23 (2017) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/ADM_2017_23_1_a5/

[1] A. Albert, “A structure theory of Jordan algebras”, Ann. of Math. (2), 48 (1947), 546–567 | DOI | MR | Zbl

[2] S. Eilenberg, “Extension of general algebras”, Ann. Soc. Polon. Math., 21 (1948), 125–134 | MR | Zbl

[3] K. Erdmann, Blocks of Tame Representation Type and Related Algebras, Lecture Notes in Mathematics, 1428, 1990 | DOI | MR | Zbl

[4] AMS Translations, 128 | MR | Zbl

[5] Yu. Drozd, V. Kirichenko, Finite-Dimensional Algebras, Springer-Verlag, Berlin, 1994 | MR | Zbl

[6] P. Gabriel, “Indecomposable Representations II”, Symposia Mathematica, XI, Academic Press, London, 1973, 81–104 | MR

[7] M. Gel'fand, V. A. Ponomarev, “Indecomposable representation of the Lorentz group”, Russian Mathematical Surveys, 23 (1968), 1–58 | DOI | MR | Zbl

[8] N. Jacobson, “Structure of alternative and Jordan bimodules”, Osaka Math. J., 6 (1954), 1–71 | MR | Zbl

[9] N. Jacobson, “Structure and representations of Jordan algebras”, AMS Colloq. Publ., 39, AMS, Providence, 1968 | DOI | MR | Zbl

[10] P. Jordan, J. von Neumann, E. Wigner, “On an algebraic generalization of quantum mechanical formalism”, Ann. of Math. (2), 36 (1934), 29–64 | DOI | MR

[11] I. Kashuba, S. Ovsienko, I. Shestakov, “Representation type of Jordan algebras”, Adv. Math., 226:1 (2011), 385–418 | DOI | MR | Zbl

[12] I. Kashuba, I. Shestakov, “Jordan Algebras of Dimension Three: Geometric Classification and Representation Type”, Actas del XVI Coloquio Latinoamericano de Álgebra, Revista Matemática Iberoamericana, 2007, 295–315 | MR | Zbl

[13] I. Kashuba, V. Serganova, “On the Tits-Kantor-Koecher construction of unital Jordan bimodules”, J. Algebra, 481 (2017), 420–463 | DOI | MR | Zbl

[14] L. Nazarova, “Representations of quivers of infinite type”, Izv. Akad. Nauk SSSR Ser. Mat., 37 (1973), 752–791 | MR | Zbl

[15] C. M. Ringel, “The Representation Type of Local Algebras”, Lecture Notes, 488, Springer, 1975, 282–305