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/s13373-014-0061-7Search in Google Scholar

[2] G. Abrams, P. Ara and M. Siles Molina, Leavitt Path Algebras, Lecture Notes in Math. 2191, Springer, London, 2017. 10.1007/978-1-4471-7344-1Search 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.2005.07.028Search 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/s11856-008-1014-1Search 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/S0002-9947-2014-05878-9Search 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/S0002-9947-2011-05264-5Search 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-2015-0241Search in Google Scholar

[8] A. S. Amitsur and J. Levitzki, Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449–463. 10.1090/S0002-9939-1950-0036751-9Search 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-zSearch 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-2011-0134Search 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/S0002-9947-2013-05717-0Search 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/649Search 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.2007.06.001Search 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.2009.58.3516Search 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/13439Search 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/s11856-018-1816-8Search 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/S0002-9939-1993-1139475-8Search 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/S021949881550125XSearch 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/trans2/006/02Search 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-XSearch 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.2003.12.018Search 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.2018.06.016Search 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)90114-9Search 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_26Search 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.2017.06.044Search 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/S0002-9947-1973-0325658-5Search 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-XSearch in Google Scholar

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

[29] M. Mirzakhani, A simple proof of a theorem of Schur, Amer. Math. Monthly 105 (1998), no. 3, 260–262. 10.1080/00029890.1998.12004879Search 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/jdr073Search in Google Scholar

[31] M. L. Racine, On maximal subalgebras, J. Algebra 30 (1974), 155–180. 10.1016/0021-8693(74)90198-7Search 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/S0002-9939-1978-0453796-5Search in Google Scholar

[33] I. Raeburn, Graph Algebras, CBMS Reg. Conf. Ser. Math. 103, American Mathematical Society, Providence, 2005. 10.1090/cbms/103Search 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_5Search 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/7821Search 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.2010.04.031Search 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.2017.07.030Search in Google Scholar