bibliography.bib

@article{albert_muckenhoupt_matrices_trace_zero,
	title         = {On matrices of trace zeros},
	author        = {Albert, A. A. and Muckenhoupt, Benjamin},
	journaltitle  = {Michigan Mathematical Journal},
	volume        = {4},
	number        = {1},
	pages         = {1--3},
	year          = {1957},
	url           = {https://projecteuclid.org/euclid.mmj/1028990168},
	urldate       = {2020-11-18},
	doi           = {10.1307/mmj/1028990168}
}

@article {diamond_lemma,
	title         = {The Diamond Lemma for Ring Theory},
	author        = {Bergman, George M.},
	journaltitle  = {Advances in Mathematics},
	volume        = {29},
	number        = {2},
	pages         = {178--218},
	date          = {1978-02},
	issn          = {0001-8708},
	doi           = {10.1016/0001-8708(78)90010-5}
}

@article{diximier_representations_lie_nilpotent,
	author        = {Dixmier, J.},
	title         = {Représentations irréductibles des algèbres de Lie nilpotentes},
	journaltitle  = {Anais da Academia Brasileira de Ciências},
	volume        = {35},
	year          = {1963},
	pages         = {491--519},
}

@article{gerstenhaber_cohomology_of_associative_ring,
	title         = {The Cohomology Structure of an Associative Ring},
	author        = {Gerstenhaber, Murray},
	journaltitle  = {Annals of Mathematics},
	volume        = {78},
	number        = {2},
	pages         = {267--288},
	year          = {1963},
	url           = {http://www.jstor.org/stable/1970343},
	urldate       = {2019-04-23},
	doi           = {10.2307/1970343}
}

@article{quillen_endomorphism_simple_module_enveloping_algebra,
	title         = {On the endomorphism ring of a simple module over an enveloping algebra},
	author        = {Quillen, Daniel},
	journaltitle  = {Proceedings of the American Mathematical Society},
	volume        = {21},
	year          = {1969},
	pages         = {171--172},
	doi           = {10.1090/S0002-9939-1969-0238892-4}
}

@article{sierra_walten_uea_witt_not_noetherian,
	title         = {The universal enveloping algebra of the Witt algebra is not noetherian},
	author        = {Susan J. Sierra and Chelsea Walton},
	journaltitle  = {Advances in Mathematics},
	volume        = {262},
	pages         = {239--260},
	date          = {2014-09-10},
	issn          = {0001-8708},
	doi           = {10.1016/j.aim.2014.05.007},
}

@book{bourbaki_algebra_1,
	title         = {Algebra~I},
	subtitle      = {Chapters~1--3},
	author        = {Bourbaki, Nicolas},
	pagetotal     = {xxiii+709},
	year          = {1989},
	publisher     = {Springer-Verlag},
	location      = {Berlin, Heidelberg, New York},
	series        = {Elements of Mathematics},
	edition       = {2nd printing},
	isbn          = {978-3-540-64243-5},
	origlanguage  = {french},
	origdate      = {1989},
	origpublisher = {Masson},
	origlocation  = {Paris}
}

@book{goodearl_warfield_introduction_to_nn_rings,
	title     = {An Introduction to Noncommutative Noetherian Rings},
	author    = {Goodearl, Ken R. and Warfield, Jr, Robert B.},
	year      = {2004},
	edition   = {2},
	series    = {London Mathematical Society Student Texts},
	number    = {61},
	publisher = {Cambridge University Press},
	doi       = {10.1017/CBO9780511841699}
}

@book{humphreys,
	title     = {Introduction to Lie Algebras and Representation Theory},
	author    = {Humphreys, James E.},
	pagetotal = {xiii+173},
	year      = {1972},
	publisher = {Springer Verlag},
	location  = {New York},
	series    = {Graduate Texts in Mathematics},
	number    = {9},
	isbn      = {978-0-387-90053-7},
	doi       = {10.1007/978-1-4612-6398-2}
}

@book {knapp_lie_and_cohomology,
	title     = {Lie Groups, Lie Algebras, and Cohomology},
	author    = {Knapp, Anthony W.},
	date      = {1988-05-21},
	pagetotal = {xii+509},
	publisher = {Princeton University Press},
	location  = {Princeton, New Jersey},
	series    = {Mathematical Notes},
	number    = {34},
	isbn      = {978-0-6910-8498-5}
}

@book{kumar_lie_cohomology,
	title     = {Kac--Moody Groups, their Flag Varieties and Representation Theory},
	author    = {Kumar, Shrawan},
	pagetotal = {xv+609},
	year      = {2002},
	edition   = {1},
	publisher = {Birkhäuser},
	location  = {Basel},
	series    = {Progress in Mathematics},
	number    = {204},
	isbn      = {978-0-8176-4227-3},
	doi       = {10.1007/978-1-4612-0105-2}
}

@book{mcconnel_noncommutative_noetherian_rings,
	title     = {Noncommutative Noetherian Rings},
	author    = {McConnel, J. C. and Robson, J. C. and Small, L. W.},
	pagetotal = {xx+636},
	publisher = {American Mathematical Society},
	series    = {Graduate Studies in Mathematics},
	number    = {30},
	edition   = {Revised edition},
	year      = {2001},
	isbn      = {978-0-8218-2169-5},
	doi       = {10.1090/gsm/030}
}

@book {serre_trees,
	title         = {Trees},
	author        = {Serre, Jean-Pierre},
	pages         = {ix+142},
	year          = {1980},
	publisher     = {Springer-Verlag},
	location      = {Berlin, Heidelberg},
	isbn          = {978-3-540-44237-0},
	doi           = {10.1007/978-3-642-61856-7},
	origlanguage  = {french},
	translator    = {Stillwell, John},
	origtitle     = {Arbres, amalgames, $\operatorname{SL}_2$},
	origsubtitle  = {Cours au Collège de France }, % this entry doesn’t exist
	origdate      = {1977},
	origpublisher = {Société Mathématique France}
}

@book{weibel_homological_algebra,
	title     = {An Introduction to Homological Algebra},
	author    = {Weibel, Charles A.},
	year      = {1994},
	pagetotal = {xiv+450},
	publisher = {Cambridge University Press},
	series    = {Cambridge Studies in Advanced Mathematics},
	number    = {38},
	isbn      = {978-0-521-55987-1},
	doi       = {10.1017/CBO9781139644136}
}

@collection{selected_works_shirshov,
	title     = {Selected Works of A.I. Shirshov},
	editor    = {Bokut, Leonid A. and Latyshev, Victor and Shestakov, Ivan and Zelmanov, Efim},
	pagetotal = {ix+242},
	year      = {2009},
	publisher = {Birkhäuser},
	location  = {Basel},
	series    = {Contemporary Mathematicians},
	isbn      = {978-3-7643-8857-7},
	doi       = {10.1007/978-3-7643-8858-4}
}
}

@incollection{shirshov_subalgebras_of_free_lie_algebras,
	crossref      = {selected_works_shirshov},
	title         = {Subalgebras of Free Lie Algebras},
	author        = {Shirshov, Anatoly Illarionovich},
	pages         = {3--14},
	origtitle     = {Подалгебры свободных алгебр Ли},
	origlanguage  = {russian},
	origdate      = {1953},
	translator    = {Bremner, Murray and Kotchetov, Mikhail V.}
}

@online{alekseevsky_michor_ruppert_extension_of_lie_algebras,
	title         = {Extensions of Lie algebras},
	author        = {Alekseevsky, Dmitri and Michor, Peter W. and Ruppert, Wolfgang},
	version       = {3},
	date          = {2000-05-04},
	eprint        = {math/0005042v3},
	eprinttype    = {arxiv},
	eprintclass   = {math.DG},
	urldate       = {2020-05-10}
}

@online {associated_generated,
	title         = {Generators of associated graded algebra},
	author        = {Lewis Topley},
	howpublished  = {MathOverflow},
	date          = {2015-11-24},
	url           = {https://mathoverflow.net/q/224454},
	urldate       = {2019-04-12},
	label         = {MO}
}

@online{nlab_extension_of_lie_algebras,
	title         = {Lie algebra extension},
	howpublished  = {nLab},
	date          = {2020-03-28},
	url           = {https://ncatlab.org/nlab/show/Lie+algebra+extension#classification_by_nonabelian_lie_algebra_cohomology},
	urldate       = {2020-05-10},
	label         = {nLab}
}

@online{nlab_nonabelian_lie_algebra_cohomology,
	title         = {nonabelian Lie algebra cohomology},
	howpublished  = {nLab},
	date          = {2019-04-02},
	url           = {https://ncatlab.org/nlab/show/nonabelian+Lie+algebra+cohomology#nonabelian_2cocycles},
	urldate       = {2020-05-10},
	label         = {nLab}
}

@online {pbw_deformation,
	title         = {Nice proofs of the Poincar\'{e}--Birkhoff--Witt theorem},
	author        = {user25309},
	howpublished  = {MathOverflow},
	date          = {2017-05-07},
	url           = {https://mathoverflow.net/q/269192},
	urldate       = {2019-04-15},
	label         = {MO}
}



### UNUSED

@online {brown,
	AUTHOR  = {Brown, Ken},
	TITLE   = {Hopf Algebras},
	NOTE    = {Lecture notes},
	URL     = {http://www.maths.gla.ac.uk/~kab/Hopf lects 1-8.pdf},
	URLDATE = {2019-04-03}
}

@book {bourbaki_lie,
	TITLE     = {Lie Groups and Lie Algebras},
	SUBTITLE  = {Chapters~1--3},
	SERIES    = {Elements of Mathematics},
	AUTHOR    = {Bourbaki, Nicolas},
	PUBLISHER = {Springer-Verlag Berlin Heidelberg New York},
	YEAR      = {1989},
	EDITION   = {2nd printing},
	ISBN      = {3-540-50218-1}
}

@book {lectures_on_sl2_modules,
	AUTHOR    = {Mazorchuk, Volodymyr},
	TITLE     = {Lectures on {$\mathfrak{sl}_2(\mathbb{C})$}-modules},
	PUBLISHER = {Imperial College Press, London},
	YEAR      = {2010},
	PAGES     = {x+263},
	ISBN      = {978-1-84816-517-5}
}

@book {tauvel_yu,
	TITLE     = {Lie Algebras and Algebraic Groups},
	AUTHOR    = {Tauvel, Patrice and Yu, Rupert W. T.},
	PAGES     = {xvi+656},
	EDITION   = {1},
	PUBLISHER = {Springer-Verlag Berlin Heidelberg},
	SERIES    = {Springer Monographs in Mathematics},
	YEAR      = {2005},
	ISBN      = {978-3-540-24170-6},
	DOI       = {10.1007/b139060}
}

@book {winter,
	TITLE     = {Abstract Lie Algebras},
	AUTHOR    = {Winter, David J.},
	PUBLISHER = {The MIT Press},
	YEAR      = {1972},
	ISBN      = {0-262-23051-8}
}

@online {semidirect_jacobi,
	TITLE         = {Semi-direct product Lie algebra},
	AUTHOR        = {Dietrich Burde},
	HOWPUBLISHED  = {Mathematics Stack Exchange},
	DATE          = {2016-03-05},
	URL           = {https://math.stackexchange.com/q/1684527},
	URLDATE       = {2019-04-08},
	LABEL         = {MS}
}