Skip to content
Permalink
Browse files

Added the PBW theorem.

  • Loading branch information...
cionx committed Apr 15, 2019
1 parent f8f77a2 commit a588c89f8a568253a1d52ad5d4e5162f440c5851
Showing with 1,336 additions and 423 deletions.
  1. +3 −1 generalstyle.sty
  2. +2 −0 glossarylist.tex
  3. +32 −0 references.bib
  4. +1,299 −422 sections/universal_enveloping_algebra.tex
@@ -132,7 +132,7 @@
\setlist[enumerate, 1]{leftmargin=*, align=left, label=\arabic*)}
\setlist[enumerate, 2]{leftmargin=*, align=left, label=\alph*)}
\setlist[description, 1]{leftmargin=\labelwidth, font=\normalfont\itshape}
\setlist[description, 2]{leftmargin=\labelwidth}
\setlist[description, 2]{leftmargin=\labelwidth, font=\normalfont\itshape}
\setlist[itemize, 1]{leftmargin=*}
\setlist[itemize, 2]{leftmargin=*,label={\textopenbullet}}

@@ -150,6 +150,7 @@
\newcommand{\adsemisimple}{$\ad$\nobreakdash-semisimple}
\newcommand{\algebra}[1]{#1\nobreakdash-algebra}
\newcommand{\algebras}[1]{#1\nobreakdash-algebras}
\newcommand{\basis}[1]{#1\nobreakdash-basis}
\newcommand{\bilinear}[1]{#1\nobreakdash-bilinear}
\newcommand{\derivation}[1]{#1\nobreakdash-derivation}
\newcommand{\dimensional}[1]{#1\nobreakdash-dimensional}
@@ -173,6 +174,7 @@
\newcommand{\subalgebra}[1]{#1\nobreakdash-subalgebra}
\newcommand{\subrepresentation}[1]{#1\nobreakdash-subrepresentation}
\newcommand{\subrepresentations}[1]{#1\nobreakdash-subrepresentation}
\newcommand{\threedimensional}{three\nobreakdash-dimensional}
\newcommand{\twococycle}{$2$\nobreakdash-cocycle}
\newcommand{\twococycles}{$2$\nobreakdash-cocycles}
\newcommand{\twodimensional}{two\nobreakdash-dimensional}
@@ -1,4 +1,5 @@
\glsxtrnewsymbol[description={adjoint representation}]{adjoint representation}{\ensuremath{\ad}}
\glsxtrnewsymbol[description={associated graded algebra of~$\glie$}]{associated graded}{\ensuremath{\gr(A)}}
\glsxtrnewsymbol[description={the space of bilinear forms~$V \times W \to \kf$}]{bilinear forms}{\ensuremath{\BF(V,W)}}
\glsxtrnewsymbol[description={center of~$\glie$}]{center}{\ensuremath{\centerlie(\glie)}}
\glsxtrnewsymbol[description={$i$-th term of the central series of~$\glie$}]{central series}{\ensuremath{\glie^i}}
@@ -22,6 +23,7 @@
\glsxtrnewsymbol[description={monoid algabra of~$M$}]{monoid algebra}{\ensuremath{\kf[M]}}
\glsxtrnewsymbol[description={nilpotent part of~$x$}]{nilpotent part}{\ensuremath{x_n}}
\glsxtrnewsymbol[description={normalizer of~$U$ in~$\glie$}]{normalizer}{\ensuremath{\normallie_{\glie}(U)}}
\glsxtrnewsymbol[description={ordered monomial in~$(x_i)_{i \in I}$}]{ordered monomial}{\ensuremath{x_\alpha}}
\glsxtrnewsymbol[description={Ore extension}]{ore extension}{\ensuremath{R[t;\sigma,\delta]}}
\glsxtrnewsymbol[description={product of~$\glie$ and~$\hlie$}]{product of lie algebras}{\ensuremath{\glie \times \hlie}}
\glsxtrnewsymbol[description={quotient Lie~algebra of~$\glie$ by~$I$}]{quotient lie algebra}{\ensuremath{\glie/I}}
@@ -40,6 +40,38 @@ @online{associated_generated
LABEL = {MO}
}

@book {trees,
TITLE = {Trees},
AUTHOR = {Serre, Jean-Pierre},
ORIGLANGUAGE = {french},
TRANSLATOR = {Stillwell, John},
YEAR = 1980,
PAGES = {ix+142},
PUBLISHER = {Springer-Verlag Berlin Heidelberg},
DOI = {10.1007/978-3-642-61856-7}
}

@article {diamond_lemma,
TITLE = {The Diamond Lemma for Ring Theory},
AUTHOR = {Bergman, George M.},
Journal = {Advances in Mathematics},
VOLUME = {29},
NUMBER = {2},
PAGES = {178--218},
YEAR = {1978},
DOI = {10.1016/0001-8708(78)90010-5}}
}

@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}
}

@book {Lectures_on_sl2_modules,
AUTHOR = {Mazorchuk, Volodymyr},
TITLE = {Lectures on {$\mathfrak{sl}_2(\mathbb{C})$}-modules},
Oops, something went wrong.

0 comments on commit a588c89

Please sign in to comment.
You can’t perform that action at this time.