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Any affine group scheme is the spectrum of a commutative Hopf algebra ( over a base S, this is given by the relative spectrum of an O < sub > S </ sub >- algebra ).

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## Some Related Sentences

Any and affine

__Any__action

**of**

**the**

**group**

**by**continuous

__affine__transformations on

**a**compact convex subset

**of**

**a**

**(**separable ) locally convex topological vector space has

**a**fixed point.

Any and group

__Any__normal subgroup has

**a**corresponding quotient

__group__

**,**formed from

**the**larger

__group__

**by**eliminating

**the**distinction between elements

**of**

**the**subgroup.

__Any__formal or informal

__group__—

**a**family

**,**

**a**church

**,**

**a**club

**,**

**a**business

**,**

**a**trade union — may be said to have government.

*

__Any__simply connected solvable Lie__group__**is**isomorphic to**a**closed subgroup**of****the**__group__**of**invertible upper triangular matrices**of**some rank**,**and any finite dimensional irreducible representation**of**such**a**__group__**is**1 dimensional.
*

__Any__simply connected nilpotent Lie__group__**is**isomorphic to**a**closed subgroup**of****the**__group__**of**invertible upper triangular matrices with 1's on**the**diagonal**of**some rank**,**and any finite dimensional irreducible representation**of**such**a**__group__**is**1 dimensional.__Any__Lie

__group__G can be decomposed into discrete

**,**simple

**,**and abelian groups in

**a**canonical way as follows.

#

__Any__tangent vector at**the**identity**of****a**Lie__group__can be extended to**a**left invariant vector field**by**left translating**the**tangent vector to other points**of****the**manifold.
"

__Any__attempt to organize**the**__group__... under**a**single authority would eliminate their independent initiatives**,**and thus reduce their joint effectiveness to that**of****the**single person directing them from**the**centre.__Any__symmetry

__group__whose elements have

**a**common fixed point

**,**which

**is**true for all finite symmetry groups and also for

**the**symmetry groups

**of**bounded figures

**,**can be represented as

**a**subgroup

**of**orthogonal

__group__

**O**

**(**n )

**by**choosing

**the**origin to be

**a**fixed point.

However

**,**in**the**case**of****a**finitely presented__group__we know that not all**the**generators can be trivial**(**__Any__individual generator could be**,****of**course**).**__Any__

__group__that managed to find ways

**of**reasoning effectively would reap benefits for all its members

**,**increasing their fitness.

__Any__time during

**a**triad conversation

**,**

__group__members can switch seats and one

**of**

**the**co-pilots can sit in

**the**pilot ’ s seat.

__Any__

__group__can be seen as

**a**category with

**a**single object in which every morphism

**is**invertible

**(**for every morphism f there

**is**

**a**morphism g that

**is**both left and right inverse to f under composition )

**by**viewing

**the**

__group__as acting on itself

**by**left multiplication.

Any and scheme

__Any__comprehensive

__scheme__

**of**accounting reform

**is**

**a**major professional and academic enterprise ; Typically it requires examination

**of**

**the**role

**of**each

**of**

**the**fundamental factors

**of**production

**,**

**an**analysis

**of**capital indicating how many types there are and how each supports each factor

**of**

**a**production process.

__Any__additional enmity that would be earned from territorial concessions was downplayed as marginal and insignificant in

**the**overall

__scheme__

**of**things.

__Any__

__scheme__

**S**has

**a**unique morphism to Spec

**(**Z ), so

**this**attitude

**,**part

**of**

**the**

**relative**point

**of**view

**,**doesn't lose anything.

__Any__

**group**

__scheme__admits natural left and right actions on its underlying

__scheme__

**by**multiplication and conjugation.

__Any__

**group**

__scheme__G

**of**finite type

**is**

**an**extension

**of**

**the**connected component

**of**

**the**identity

**(**i. e.,

**the**maximal connected subgroup

__scheme__)

**by**

**a**constant

**group**

__scheme__.

__Any__complete

**group**variety

**(**variety here meaning reduced and geometrically irreducible separated

__scheme__

**of**finite type

**over**

**a**field )

**is**automatically

**commutative**

**,**

**by**

**an**argument involving

**the**action

**of**conjugation on jet spaces

**of**

**the**identity.

__Any__backup

__scheme__has some labor requirement

**,**but complicated schemes have considerably higher labor requirements.

__Any__Tibetan language romanization

__scheme__

**is**faced with

**a**dilemma: should it seek to accurately reproduce

**the**sounds

**of**spoken Tibetan

**,**or

**the**spelling

**of**written Tibetan?

__Any__editing application which supports NTSC video can be used to edit footage employing

**the**3: 2 pulldown

__scheme__.

__Any__decision taken under

**this**

__scheme__will require

**the**support

**of**at least 55 %

**of**

**the**Council

**of**

**the**European Union members who must also represent at least 65 %

**of**

**the**EU's citizens.

__Any__new

__scheme__would use

**a**smarycatd which would then be usable in-at least-all Dublin public transport systems.

__Any__compulsory

__scheme__

**of**data retention would also be affected

**by**Article 8

**(**

**the**respect for

**the**right

**of**privacy )

**of**

**the**European Convention on Human Rights.

__Any__reduced

__scheme__has

**a**normalization

**,**whose construction we first give for irreducible reduced schemes.

Any and is

__Any__claimant whose claim

__is__denied

**,**or

__is__approved for less than

**the**full amount

**of**such claim

**,**shall be entitled

**,**under such regulations as

**the**Commission may prescribe

**,**to

**a**hearing before

**the**Commission

**,**or its duly authorized representatives

**,**with respect to such claim.

__Any__alteration

**of**one

**of**these factors

__is__distortion

**,**although we generally use that word only for effects so pronounced that they can be stated quantitatively on

**the**basis

**of**standard tests.

__Any__musician playing Beethoven here

**,**where Beethoven was born

**,**

__is__likely to examine his own interpretations with special care.

__Any__action

__is__understood to create " seeds " in

**the**mind that sprout into

**the**appropriate results

**(**Pāli vipaka ) when they meet

**the**right conditions.

__Any__information may be conveyed

**by**

**an**analog signal ; often such

**a**signal

__is__

**a**measured response to changes in physical phenomena

**,**such as sound

**,**light

**,**temperature

**,**position

**,**or pressure.

__Any__quantity

**of**energy absorbed

**by**

**the**electron in excess

**of**

**this**amount

__is__converted to kinetic energy according to

**the**conservation

**of**energy.

__Any__breach

**of**these laws

__is__

**a**criminal offence and can lead to fine

**of**up to £ 5

**,**000 or six months in prison.

The prohibition against retaliation or coercion applies broadly to any individual or entity that seeks to prevent

**an**individual from exercising his or her rights or to retaliate against him or her for having exercised those rights ...__Any__form**of**retaliation or coercion**,**including threats**,**intimidation**,**or interference**,**__is__prohibited if it__is__intended to interfere.__Any__work

**(**δW ) done must be done at

**the**expense

**of**internal energy U

**,**since no heat δQ

__is__being supplied from

**the**surroundings.

"

__Any__threat**of**war Clovis could make would only be effective if they were neighbors ; " it__is__nowhere written that Syagrius was handed**over**in 486 or 487.__Any__player may declare

**the**game

**over**at any time during his turn if either

**of**two conditions

__is__true: one chain has 41 or more tiles

**,**or there

__is__at least one chain on

**the**board and every chain on

**the**board has 11 or more tiles.

1.496 seconds.