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...cs)|group]] ''G'' on a [[algebra over a field|''k''-algebra]] ''A'' is a [[linear representation]] <math>\pi: G \to GL(A)</math> such that, for each ''g'' in ...ons|representation put on]] the [[tensor algebra]] <math>T(A)</math> is an algebraic representation of ''G''. ...

...r1=Friedlander, Eric |editor2=Grayson, Daniel |chapter=Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry}}</ref> ...year=1972|pages=552–586}}</ref> showing in particular that they are finite groups. ...

...rn}} is a mathematician specializing in the [[representation theory]] of [[algebraic group]]s. She is a professor of mathematics at the [[École Polytechnique Fé ...egon]] in 1985. Her dissertation, ''Certain Embeddings of Simple Algebraic Groups'', was supervised by [[Gary Seitz]].{{r|mg}} As a faculty member at [[Wesle ...

...rems asserting that the [[group cohomology|group homology]] of a series of groups <math>G_1 \subset G_2 \subset \cdots </math> is stable, i.e., ...of the groups ''K''_''i'' of rings of algebraic integers.|title=Algebraic K-theory, I: Higher K-theories|pages=179–198|series=Lecture Notes in Math.| ...

...|first=Spencer |date=2006-07-23 |title=Algebraic Cycles and Additive Chow Groups |url=http://www.math.uchicago.edu/~bloch/addchow_rept.pdf |publisher=Dept. The additive K-functors are related to [[cyclic homology]] groups by the isomorphism ...

{{Short description|Linear function satisfying a support condition}} ...the [[Lie group–Lie algebra correspondence]] and its variant for algebraic groups in the characteristic zero; for example, this approach taken in {{harv|Jant ...

...an [[algebraic variety]] is a [[group-scheme action|group action]] of an [[algebraic torus]] on the variety. A variety equipped with an action of a torus ''T'' A [[normal scheme|normal]] algebraic variety with a torus acting on it in such a way that there is a dense orbit ...

...s used to define the [[Kirillov model]] of a representation of the general linear group. ...element of {{mvar|k}} is a mirabolic subgroup of the 2-dimensional general linear group. ...

{{Lie groups |Semi-simple}} == Real forms for Lie groups and algebraic groups == ...

...are used in the theory of [[Lattice (discrete subgroup)|lattices]] in Lie groups, often under the name ''field of definition''. == Fuchsian and Kleinian groups == ...

...'', introduced by [[Serge Lang]], states: if ''G'' is a connected smooth [[algebraic group]] over a [[finite field]] <math>\mathbf{F}_q</math>, then, writing <m ...rivial one. Also, the theorem plays a basic role in the theory of [[finite groups of Lie type]]. ...

...r an infinite [[Field (mathematics)|field]] ''k'' is a [[polynomial]] in [[linear functional]]s with coefficients in ''k''; i.e., it can be written as where the <math>\lambda_{i_j}: V \to k</math> are linear functionals and the <math>w_{i_1, \dots, i_n}</math> are vectors in ''W''. ...

...lattice (discrete subgroup)|lattice]]: it may be a so-called [[thin group (algebraic group theory)|thin group]]. The "gap" in question is a lower bound (absolut ...linear group]] over the integers, and in more general classes of algebraic groups ''G'', is that the sequence of [[Cayley graph]]s for reductions Γ<sub>''p'' ...

...] of a compact complex manifold to a sum over its [[Dolbeault cohomology]] groups. *The linear transformation ''A''_''p'' is the action induced by ''f'' on the ...

...h deals with algebraic K-theory and the representation theory of algebraic groups, among other topics. He has frequently been a visiting professor at [[North ...>{{cite journal|doi=10.1007/BF01390018|title=Homology stability for linear groups|year=1980|last1=van der Kallen|first1=Wilberd|journal=Inventiones Mathemati ...

...braic scheme ''X'' with [[linear algebraic group action|action of a linear algebraic group]] ''G'', via Quillen's [[Q-construction]]; thus, by definition, ...1=Krishna|first1=Amalendu|last2=Ravi|first2=Charanya|date=2017-08-02|title=Algebraic K-theory of quotient stacks|eprint=1509.05147|class=math.AG}}</ref> (Hence, ...

...h good properties even if ''X'' is a [[linear variety (algebraic geometry)|linear variety]], roughly a variety admitting a cell decomposition. He also notes ...ournal |last1=Totaro |first1=Burt |title=Chow groups, Chow cohomology, and linear varieties |journal=Forum of Mathematics, Sigma |date=1 June 2014 |volume=2 ...

...guage=de | trans-title=Algebraic points on analytic subgroups of algebraic groups | title=Algebraische Punkte auf analytischen Untergruppen algebraischer Gru ...less <math>A</math> contains a proper [[Algebraic group#Algebraic subgroup|algebraic subgroup]]. ...

...cite book | last=Hatcher | first=Allen | author-link=Allen Hatcher | title=Algebraic Topology | publisher=[[Cambridge University Press]] | year=2002 | isbn=0-52 ...ategory of rings|rings]]. This means that each space is associated with an algebraic structure, while each continuous map between spaces is associated with a st ...

== Second fundamental theorem for general linear group == generated by the [[determinant]]s of all the <math>k \times k</math>-[[minor (linear algebra)|minor]]s.<ref>{{harvnb|Procesi|2007|loc=Ch. 11, § 5.1.}}</ref><!-- ...