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...math>\mathfrak{gl}(n)</math> the [[General linear group|general linear Lie algebra]] and <math> I_n </math> the <math> n \times n </math> [[identity matrix] ...\mathfrak{gl}(n+1) : \text{tr}(x) = 0 \} </math>, the ''special linear Lie algebra''; ...

* [[Special linear Lie algebra]] <math>\mathfrak{sl}_2</math> * the mathematical structure SL₂(''F''), a [[special linear group]] ...

In [[abstract algebra]], it refers to a family of concepts: * A <math>I</math>-[[graded vector space]] or '''graded linear space''' is thus a [[vector space]] with a decomposition into a [[direct su ...

That is, all super diagonals of <math>T_0</math> consist of zeros, the main diagonal consists ...tephen |last1=Soltys |first1=Michael |title=The Proof Complexity of Linear Algebra |journal=Annals of Pure and Applied Logic |volume=130 |issue=1–3 |date=Dece ...

The [[Lie algebroid differential]] is an '''''<math>\mathbb{R}</math>'''''-linear operator ''<math>d_A</math>'' on the ''<math>A</math>''-forms ''<math>\Omeg # A [[Lie bialgebra]] consists of two [[Lie algebra]]s ''<math>(\mathfrak{g},[\cdot,\cdot]_{\mathfrak{g}})</math>'' and ''<math ...

...the [[tangent space]]. The concept generalizes the notion of [[Frobenius algebra]] to tangent bundles. ...manifold (''M'',&nbsp;''g'',&nbsp;*) with constant product is a Frobenius algebra ''M''. ...

...Therefore, a differential graded Lie algebra can be seen as a homotopy Lie algebra where the Jacobi identity holds on the nose. These homotopy algebras are us ...s more than others. The most traditional definition is via symmetric multi-linear maps, but there also exists a more succinct geometric definition using the ...

...ered in mathematics, such as [[extension field]]s, [[polynomial ring]]s, [[algebra over a field|algebras]] and [[function space]]s. The term ''vector'' is gen ==Vectors in algebra== ...

...re is natural definition of the [[determinant]] for them and most [[linear algebra]] theorems like [[Cramer's rule]], [[Cayley–Hamilton theorem]], etc. hold t ...l construction of "non-commutative symmetries" which can be applied to any algebra. ...

...be used to write down new such quantum groups by using the [[Braided Hopf algebra|Radford biproduct]].<ref name="AS02" /> ...s and [[Dynkin diagram]]s, strikingly similar to those of [[semisimple Lie algebra]]s.<ref name=HS08/> A comprehensive introduction is found in the lecture of ...

...tability of 1-D systems because, for example, the [[fundamental theorem of algebra]] does not exist in the [[Ring (mathematics)|ring]] of ''m''-D (''m''&nbsp; == Linear multidimensional state-space model == ...

...odel]], [[N = 1 supersymmetric Yang–Mills theory|<math>\mathcal N=1</math> super Yang–Mills theory]], and the [[Minimal Supersymmetric Standard Model]]. Whe ...ontent of this theory must belong to representations of the super-Poincaré algebra, known as supermultiplets.<ref>{{cite book|last=Weinberg|first=S.|author-li ...

| OEIS_name = Little Schroeder numbers,<br/>Super Catalan They are also called the '''super-Catalan numbers''', the '''little Schröder numbers''', or the '''Hipparchus ...

...inition typically involves a [[Hilbert space]], an [[algebra (ring theory)|algebra]] of operators on it and an unbounded [[self-adjoint]] operator, endowed wi ...se part of the Dirac operator, in conjunction with the [[function algebra|algebra of functions]], gives a K-cycle which encodes index-theoretic information. ...

...modular forms''' associated to a [[subgroup]] {{math|Γ}} of the [[special linear group]] {{math|SL(2, '''Z''')}} is the [[graded ring]] generated by the [[m ...ub>(Γ)}} is isomorphic as a [[Algebra over a field|<math>\mathbb{C}</math>-algebra]] to <math>\mathbb{C}[E_4, E_6]</math>, which is the [[polynomial ring]] of ...

...ty]]. When other global (rigid) symmetries (e.g., if the theory is a [[non-linear sigma model]]) of the theory are gauged such that some (non-gravitino) fiel ...ath>2^{\lfloor n\rfloor}</math>-dimensional representation of the Clifford algebra, the representation that acts on the Dirac spinors, consists of the [[gamma ...

...amples of finite-dimensional Nichols algebras are the [[Borel subgroup#Lie algebra|Borel parts]] <math>u_q(\mathfrak{g})^+</math> of the Frobenius–Lusztig ker ...port of <math>V</math>. For more details on Nichols algebras see [[Nichols algebra]]. ...

the [[differential operator]]s <math>\ell_n</math> generate a [[Witt algebra]]. ...rediction of negative energy solutions, precisely because they generate an algebra of creation operators that can lower the energy ad infinitum. ...

...lated to the [[Lie algebra representation|representation theory of the Lie algebra]] <math>\mathfrak{gl}_n</math>. It can be used to relate an invariant ''ƒ'' ...} </math> defines a [[Lie algebra representation|representation of the Lie algebra]] <math>\mathfrak{gl}_n</math> in the vector space of polynomials of <math> ...

{{defn|no=2|A central charge of the Virasoro algebra or similar algebra.}} ...=2|A '''chiral multiplet''' is a type of supermutliplet of a supersymmetry algebra.}} ...