We classify isomorphism and similarity classes of pointed reflection spaces of residue ≤ 2. This leads to the classification of reduced extended affine root systems whose involved pointed reflection spaces have residue ≤ 2.
[1] B. Allison, S. Azam, S. Berman, Y. Gao and A. Pianzola: Extended aflne Lie gebras and their root systems, Mem. Amer. Math. Soc. 126 (1997), no. 603.
[2] S. Azam: Extended aflne root systems. J. Lie Theory 12 (2002), 515–527.
[3] S. Azam: Nonreduced extended aflne root systems of nullity 3, Comm. Algebra 25 (1997), 3617–3654.
[4] S. Azam, Y. Khalili and M. Yousofzadeh: Extended aflne root systems of type BC, J. Lie Theory 15 (2005), 145–181.
[5] S. Azam and V. Shahsanaei: Extended aflne Weyl groups of type A1, J. Algebraic Combin. 28 (2008), 481–493.
[6] S. Azam, M.B. Soltani, M. Tomie and Y. Yoshii: A graph-theoretical classification for reflectable bases, Publ. Res. Inst. Math. Sci. 55 (2019), 689–736.
[7] S. Azam, H. Yamane and M. Yousofzadeh: Reflectable bases for aflne reflection systems, J. Algebra 371(2012), 63–93.
[8] O. Loos: Symmetric spaces, I: General theory, Benjamin Inc. New York, 1969.
[9] O. Loos and E. Neher: Locally finite root systems, Mem. Amer. Math. Soc. 171 (2004), no. 811.
[10] O. Loos and E. Neher: Reflections systems and partial root systems, Forum Math 23 (2011), 349–411.
[11] J. Morita and Y. Yoshii: Locally extended aflne Lie algebras, J. Algebra 301 (2006), 59–81.
[12] J. Morita and Y. Yoshii: Locally loop algebras and locally aflne Lie algebras, J. Algebra 440 (2015), 379–442.
[13] E. Neher: Extended aflne Lie algebras and other generalizations of aflne Lie algebras- a survey; in Devel- opments and Trends in Infinite-Dimensional Lie Theory, Prog. Math. 288, Birkha¨user Boston, Inc., Boston, MA, 2011, 53–126.
[14] J. Oxley: Matroid Theory, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1992.
[15] S. Saito: Extended aflne root systems I (Coxeter transformations), Publ. Rre Inst. Math. Sci. 21 (1985), 75–179.
[16] Y. Yoshii: Locally extended aflne root systems; in Quantum Affine Algebras, Extended Affine Lie Algebras and Applications, Contemp. Math. 506 (2010), 285–302.
[17] Y. Yoshii: New Lie tori from Naoi tori, Toyama Math. J. 37 (2015), 155–187.
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