Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras

References

[1] G. Abrams, Leavitt path algebras: The first decade, Bull. Math. Sci. 5 (2015), no. 1, 59–120. 10.1007/s13373-014-0061-7Suche in Google Scholar

[2] G. Abrams, P. Ara and M. Siles Molina, Leavitt Path Algebras, Lecture Notes in Math. 2191, Springer, London, 2017. 10.1007/978-1-4471-7344-1Suche in Google Scholar

[3] G. Abrams and G. Aranda Pino, The Leavitt path algebra of a graph, J. Algebra 293 (2005), no. 2, 319–334. 10.1016/j.jalgebra.2005.07.028Suche in Google Scholar

[4] G. Abrams, G. Aranda Pino and M. Siles Molina, Locally finite Leavitt path algebras, Israel J. Math. 165 (2008), 329–348. 10.1007/s11856-008-1014-1Suche in Google Scholar

[5] G. Abrams, J. P. Bell and K. M. Rangaswamy, On prime nonprimitive von Neumann regular algebras, Trans. Amer. Math. Soc. 366 (2014), no. 5, 2375–2392. 10.1090/S0002-9947-2014-05878-9Suche in Google Scholar

[6] G. Abrams and M. Tomforde, Isomorphism and Morita equivalence of graph algebras, Trans. Amer. Math. Soc. 363 (2011), no. 7, 3733–3767. 10.1090/S0002-9947-2011-05264-5Suche in Google Scholar

[7] A. L. Agore, The maximal dimension of unital subalgebras of the matrix algebra, Forum Math. 29 (2017), no. 1, 1–5. 10.1515/forum-2015-0241Suche in Google Scholar

[8] A. S. Amitsur and J. Levitzki, Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449–463. 10.1090/S0002-9939-1950-0036751-9Suche in Google Scholar

[9] P. Ara, M. A. Moreno and E. Pardo, Nonstable K-theory for graph algebras, Algebr. Represent. Theory 10 (2007), no. 2, 157–178. 10.1007/s10468-006-9044-zSuche in Google Scholar

[10] G. Aranda Pino, J. Brox and M. Siles Molina, Cycles in Leavitt path algebras by means of idempotents, Forum Math. 27 (2015), no. 1, 601–633. 10.1515/forum-2011-0134Suche in Google Scholar

[11] G. Aranda Pino, J. Clark, A. an Huef and I. Raeburn, Kumjian-Pask algebras of higher-rank graphs, Trans. Amer. Math. Soc. 365 (2013), no. 7, 3613–3641. 10.1090/S0002-9947-2013-05717-0Suche in Google Scholar

[12] G. Aranda Pino and K. Crow, The center of a Leavitt path algebra, Rev. Mat. Iberoam. 27 (2011), no. 2, 621–644. 10.4171/RMI/649Suche in Google Scholar

[13] G. Aranda Pino, D. Martín Barquero, C. Martín González and M. Siles Molina, The socle of a Leavitt path algebra, J. Pure Appl. Algebra 212 (2008), no. 3, 500–509. 10.1016/j.jpaa.2007.06.001Suche in Google Scholar

[14] G. Aranda Pino, E. Pardo and M. Siles Molina, Prime spectrum and primitive Leavitt path algebras, Indiana Univ. Math. J. 58 (2009), no. 2, 869–890. 10.1512/iumj.2009.58.3516Suche in Google Scholar

[15] L. O. Clark, C. Gil Canto and A. Nasr-Isfahani, The cycline subalgebra of a Kumjian–Pask algebra, Proc. Amer. Math. Soc. 145 (2017), no. 5, 1969–1980. 10.1090/proc/13439Suche in Google Scholar

[16] L. O. Clark, D. Martín Barquero, C. Martín González and M. Siles Molina, Using the Steinberg algebra model to determine the center of any Leavitt path algebra, Israel J. Math. 230 (2019), no. 1, 23–44. 10.1007/s11856-018-1816-8Suche in Google Scholar

[17] R. C. Cowsik, A short note on the Schur-Jacobson theorem, Proc. Amer. Math. Soc. 118 (1993), no. 2, 675–676. 10.1090/S0002-9939-1993-1139475-8Suche in Google Scholar

[18] M. Domokos and M. Zubor, Commutative subalgebras of the Grassmann algebra, J. Algebra Appl. 14 (2015), no. 8, Article ID 1550125. 10.1142/S021949881550125XSuche in Google Scholar

[19] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras (in Russian), Mat. Sbornik N. S. 30(72) (1952), 349–462. 10.1090/trans2/006/02Suche in Google Scholar

[20] A. Elduque, On maximal subalgebras of central simple Mal’cev algebras, J. Algebra 103 (1986), no. 1, 216–227. 10.1016/0021-8693(86)90181-XSuche in Google Scholar

[21] A. Elduque, J. Laliena and S. Sacristán, Maximal subalgebras of associative superalgebras, J. Algebra 275 (2004), no. 1, 40–58. 10.1016/j.jalgebra.2003.12.018Suche in Google Scholar

[22] C. Gil Canto and A. Nasr-Isfahani, The commutative core of a Leavitt path algebra, J. Algebra 511 (2018), 227–248. 10.1016/j.jalgebra.2018.06.016Suche in Google Scholar

[23] W. H. Gustafson, On maximal commutative algebras of linear transformations, J. Algebra 42 (1976), no. 2, 557–563. 10.1016/0021-8693(76)90114-9Suche in Google Scholar

[24] N. Jacobson, Schur’s theorems on commutative matrices, Bull. Amer. Math. Soc. 50 (1944), 431–436. 10.1007/978-1-4612-3692-4_26Suche in Google Scholar

[25] T. Kajiwara and Y. Watatani, Maximal abelian subalgebras of C∗-algebras associated with complex dynamical systems and self-similar maps, J. Math. Anal. Appl. 455 (2017), no. 2, 1383–1400. 10.1016/j.jmaa.2017.06.044Suche in Google Scholar

[26] D. Krakowski and A. Regev, The polynomial identities of the Grassmann algebra, Trans. Amer. Math. Soc. 181 (1973), 429–438. 10.1090/S0002-9947-1973-0325658-5Suche in Google Scholar

[27] W. G. Leavitt, The module type of a ring, Trans. Amer. Math. Soc. 103 (1962), 113–130. 10.1090/S0002-9947-1962-0132764-XSuche in Google Scholar

[28] A. I. Malcev, Commutative subalgebras of semi-simple Lie algebras, Amer. Math. Soc. Transl. 1951 (1951), no. 40, 1–15. Suche in Google Scholar

[29] M. Mirzakhani, A simple proof of a theorem of Schur, Amer. Math. Monthly 105 (1998), no. 3, 260–262. 10.1080/00029890.1998.12004879Suche in Google Scholar

[30] G. Nagy and S. Reznikoff, Abelian core of graph algebras, J. Lond. Math. Soc. (2) 85 (2012), no. 3, 889–908. 10.1112/jlms/jdr073Suche in Google Scholar

[31] M. L. Racine, On maximal subalgebras, J. Algebra 30 (1974), 155–180. 10.1016/0021-8693(74)90198-7Suche in Google Scholar

[32] M. L. Racine, Maximal subalgebras of central separable algebras, Proc. Amer. Math. Soc. 68 (1978), no. 1, 11–15. 10.1090/S0002-9939-1978-0453796-5Suche in Google Scholar

[33] I. Raeburn, Graph Algebras, CBMS Reg. Conf. Ser. Math. 103, American Mathematical Society, Providence, 2005. 10.1090/cbms/103Suche in Google Scholar

[34] J. Schur, Zur Theorie der vertauschbaren Matrizen, J. Reine Angew. Math. 130 (1905), 66–76. 10.1007/978-3-642-61947-2_5Suche in Google Scholar

[35] J. Szigeti, J. van den Berg, L. van Wyk and M. Ziembowski, The maximum dimension of a Lie nilpotent subalgebra of 𝕄n⁢(F) of index 𝐦, Trans. Amer. Math. Soc. 372 (2019), no. 7, 4553–4583. 10.1090/tran/7821Suche in Google Scholar

[36] M. Tomforde, Leavitt path algebras with coefficients in a commutative ring, J. Pure Appl. Algebra 215 (2011), no. 4, 471–484. 10.1016/j.jpaa.2010.04.031Suche in Google Scholar

[37] L. van Wyk and M. Ziembowski, Lie solvability and the identity [x1,y1]⁢[x2,y2]⁢⋯⁢[xq,yq]=0 in certain matrix algebras, Linear Algebra Appl. 533 (2017), 235–257. 10.1016/j.laa.2017.07.030Suche in Google Scholar