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@article{BL,
  title = {Three-algebras and $\mathcal{N}=6$ {C}hern-{S}imons gauge theories},
  author = {Bagger, J. and Lambert, N.},
  journal = {Phys. Rev. D},
  volume = {79},
  number = {2},
  pages = {025002},
  numpages = {8},
  year = {2009},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.79.025002},
}

@article{Ba,
title = "On the action of the symmetric group on the Free Lie Algebra and the partition lattice",
journal = "J. Combin. Theory Ser. A",
volume = "55",
number = "1",
pages = "93 - 129",
year = "1990",
doi = "10.1016/0097-3165(90)90050-7",
author = "Barcelo, H."
}

@misc{BF,
  title={One {G}arnir to rule them all: on {S}pecht modules and the {C}ata{LA}n{K}e theorem},
  author={Brauner, S. and Friedmann, T.},
  eprint={1803.1091},
  eprinttype={arxiv},
  year={2018},
}

@article{Co,
author = {Cohen, F.},
year = {1995},
pages = {19-42},
title = {On configuration spaces, their homology, and Lie algebras},
volume = {100},
journal = {J. Pure Appl. Algebra},
doi = {10.1016/0022-4049(95)00054-Z}
}

@Article{DT,
author="Daletskii, Y.L.
and Takhtajan, L.A.",
title="Leibniz and {L}ie Algebra Structures for {N}ambu Algebra",
journal="Lett. Math. Phys.",
year="1997",
volume="39",
number="2",
pages="127--141",
doi="10.1023/A:1007316732705",
}

@article{DI,
  author={J.A. de Azc\'arraga and J.M. Izquierdo},
  title={n-ary algebras: a review with applications},
  journal={J. Phys. A},
  volume={43},
  number={29},
  pages={293001},
   year={2010}
}

@article{Fi,
  title={n-{L}ie algebras},
  year={1985},
  author={Filippov, V.T.},
  journal={Sib. Mat. Zh.},
  volume={26},
  pages={126}
}

@article{fr,
  title={Orbifold singularities, {L}ie algebras of the third kind ({LATK}es), and pure {Y}ang--{M}ills with matter},
  author={Friedmann, T.},
  journal={J. Math. Phys.},
  volume={52},
  number={2},
  pages={022304, 23 pp.},
  year={2011},
  DOI = {10.1063/1.3528673},
}

@misc{FHSW1,
  title={On a generalization of {L}ie($ k $): a {C}ata{LA}n{K}e theorem},
  author={Friedmann, T. and Hanlon, P. and Stanley, R.P. and Wachs, M.L.},
  eprint={1710.00376},
  eprinttype={arxiv},
  year={2017}
}

@unpublished{FHSW2,
  note={Work in progress},
  author={Friedmann, T. and Hanlon, P. and Stanley, R.P. and Wachs, M.L.},
}


@book{Fu,
  title={Young tableaux: with applications to representation theory and geometry},
  author={Fulton, W.},
  volume={35},
  year={1997},
  publisher={Cambridge University Press}
}


@ARTICLE{Gu,
    author = {A. Gustavsson},
    title = {Algebraic structures on parallel {M}2-branes},
    JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {811},
      YEAR = {2009},
    NUMBER = {1-2},
     PAGES = {66--76},
   MRCLASS = {81T30},
  MRNUMBER = {2492260},
MRREVIEWER = {Farhang Loran},
       DOI = {10.1016/j.nuclphysb.2008.11.014},
}

@ARTICLE{Han,
    author = {P. Hanlon},
    title = {The fixed-point partition lattices},
    JOURNAL = {Pacific J. Math.},
  FJOURNAL = {Pacific Journal of Mathematics},
    VOLUME = {96},
      YEAR = {1981},
    NUMBER = {2},
     PAGES = {319--341},
   MRCLASS = {06C10 (05B35)},
  MRNUMBER = {637975},
MRREVIEWER = {R. W. Quackenbush},
       URL = {http://projecteuclid.org/euclid.pjm/1102734788},
}

@article{HW,
title = "On Lie k-Algebras",
journal = "Adv. Math.",
volume = "113",
number = "2",
pages = "206 - 236",
year = "1995",
doi = "10.1006/aima.1995.1038",
author = "P. Hanlon and M.L. Wachs"
}

@Article{Ka,
author="Kasymov, Sh.M.",
title="Theory of n-{L}ie algebras",
journal="Algebra and Logic",
year="1987",
volume="26",
number="3",
pages="155--166",
doi="10.1007/BF02009328",
}

@article{Kr,
author = {Kra\'skiewicz, W.},
year = {1995},
pages = {293-313},
title = {Reduced decompositions in Weyl groups},
volume = {16},
journal = {European J. Combin.}
}

@article{KW,
AUTHOR = {Kra\'skiewicz, W. and Weyman, J.},
     TITLE = {Algebra of coinvariants and the action of a {C}oxeter element},
   JOURNAL = {Bayreuth. Math. Schr.},
  FJOURNAL = {Bayreuther Mathematische Schriften},
    NUMBER = {63},
      YEAR = {2001},
     PAGES = {265--284},
   MRCLASS = {20C30 (05E10 17B01)},
  MRNUMBER = {1867283},
MRREVIEWER = {Christine Bessenrodt},
}

@Article{KS,
author="Kol, B. and Shir, R.",
title="Color structures and permutations",
journal="J. High Energy Phys.",
year="2014",
volume="2014",
number="11",
pages="20",
doi="10.1007/JHEP11(2014)020",
}


@phdthesis{Li,
author = {Ling, W.},
year = {1993},
title = {On the structure of $n$-{L}ie algebras},
school = {University-GHS-Siegen}
}

@book{Re,
author={Reutenauer, C.},
title={Free {L}ie algebras},
SERIES = {London Mathematical Society Monographs. New Series},
    VOLUME = {7},
      NOTE = {Oxford Science Publications},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = {1993},
     PAGES = {xviii+269},
   MRCLASS = {17-02 (05-02 17B05)},
  MRNUMBER = {1231799},
MRREVIEWER = {Hartmut Laue},
}

@article{St,
title = "Some aspects of groups acting on finite posets",
journal = "J. Combin. Theory Ser. A",
volume = "32",
number = "2",
pages = "132 - 161",
year = "1982",
doi = "10.1016/0097-3165(82)90017-6",
author = "Stanley, R.P."
}



@ARTICLE{Ta,
    author = {L. Takhtajan},
    TITLE = {On foundation of the generalized {N}ambu mechanics},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {160},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {295--315},
      ISSN = {0010-3616},
   MRCLASS = {58F05 (58F07 70G99 70H05 81S05)},
  MRNUMBER = {1262199},
MRREVIEWER = {Johannes Huebschmann},
       DOI = {10.1007/BF02103278}
}


@article{Wa,
title = "On the (co)homology of the partition lattice and the free Lie algebra",
author = "Wachs, M.L.",
year = "1998",
volume = "193",
pages = "287--319",
journal = "Discrete Math.",
publisher = "Elsevier",
number = "1-3",
DOI = {10.1016/S0012-365X(98)00147-2}
}