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* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )

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## Some Related Sentences

Every and Lie

__Every__homomorphism f: G → H

**of**

__Lie__groups induces

**a**homomorphism

**between**

**the**corresponding

__Lie__algebras

**and**.

__Every__vector v in determines

**a**linear map from R to taking 1 to v

**,**which can be thought

**of**as

**a**

__Lie__algebra homomorphism.

*****

__Every__integrable subbundle

**of**

**the**

**tangent**

**bundle**— that

**is**

**,**one whose sections are closed under

**the**

__Lie__bracket — also defines

**a**

__Lie__algebroid.

*****

__Every__

**bundle**

**of**

__Lie__algebras over

**a**smooth

**manifold**defines

**a**

__Lie__algebroid where

**the**

__Lie__bracket

**is**defined pointwise

**and**

**the**anchor map

**is**equal to zero.

Consider

**a**__Lie__algebra g over**a**field K.__Every__element x**of**g defines**the**adjoint endomorphism ad**(**x**)****(**also written as ad < sub > x </ sub >)**of**g**with****the**help**of****the**__Lie__bracket**,**as__Every__quantum field theory satisfying certain technical assumptions about

**its**S-matrix that has non-trivial interactions can only have

**a**symmetry

__Lie__algebra which

**is**always

**a**direct

**product**

**of**

**the**Poincaré

**group**

**and**

**an**internal

**group**if

**there**

**is**

**a**mass gap: no mixing

**between**these two

**is**possible.

The album features such hits as attitudized song "

__Every__Little__Lie__" which tell**a**tale**of****an**unfaithful man who instead**of**ending**the**relationship amicablely**,**decides to lead her on.

Every and group

Group actions / representations:

__Every____group__G can be considered as**a**category**with****a**single object whose morphisms are**the**elements**of**G. A functor from G to Set**is**then nothing but**a**__group__action**of**G on**a**particular set**,**i. e.**a**G-set.__Every__galaxy

**of**sufficient mass in

**the**Local Group has

**an**associated

__group__

**of**globular clusters

**,**

**and**almost every large galaxy surveyed has been found to possess

**a**system

**of**globular clusters.

__Every__instrumental

__group__

**(**or section

**)**has

**a**principal who

**is**generally responsible for leading

**the**

__group__

**and**playing orchestral solos.

*****

__Every__closed subgroup

**of**

**a**profinite

__group__

**is**

**itself**profinite ;

**the**topology arising from

**the**profiniteness agrees

**with**

**the**subspace topology.

While he admits

**the**existence**of**caste-based discrimination**,**he writes that "__Every__social__group__cannot be regarded as**a**race simply because we want to protect it against prejudice**and**discrimination ".__Every__summer

**the**

__group__gathers in Newport

**,**RI for week long dance training

**,**seaside teas

**,**

**and**evenings enjoying

**the**splendors

**of**

**the**Gilded Age.

*****

__Every__finitely generated

__group__

**with**

**a**recursively enumerable presentation

**and**insoluble word problem

**is**

**a**subgroup

**of**

**a**finitely presented

__group__

**with**insoluble word problem

__Every__synset contains

**a**

__group__

**of**synonymous words or collocations

**(**

**a**collocation

**is**

**a**sequence

**of**words that go together to form

**a**specific meaning

**,**such as " car pool "); different senses

**of**

**a**word are in different synsets.

__Every__

__group__can be trivially made into

**a**topological

__group__by considering it

**with**

**the**discrete topology ; such groups are called discrete groups.

__Every__topological

__group__can be viewed as

**a**uniform

**space**in two ways ;

**the**left uniformity turns all left multiplications into uniformly continuous maps while

**the**right uniformity turns all right multiplications into uniformly continuous maps.

__Every__subgroup

**of**

**a**topological

__group__

**is**

**itself**

**a**topological

__group__when given

**the**subspace topology.

__Every__ten years

**,**when

**the**general census

**of**population takes place

**,**each citizen has to declare which linguistic

__group__they belong or want to be aggregated to.

Every and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to

**the**closest scrutiny as

**a**test

**of**his political allegiances

**,**not his convictions.

__Every__detail in his interpretation has been beautifully thought out

**,**

**and**

**of**these I would especially cite

**the**delicious laendler touch

**the**pianist brings to

**the**fifth variation

**(**

**an**obvious indication that he

__is__playing

**with**Viennese musicians

**)**

**,**

**and**

**the**gossamer shading throughout.

__Every__taxpayer

__is__well aware

**of**

**the**vast size

**of**our annual defense budget

**and**most

**of**our readers also realize that

**a**large portion

**of**these expenditures go for military electronics.

__Every__few days

**,**in

**the**early morning

**,**as

**the**work progressed

**,**twenty men would appear to push it ahead

**and**to shift

**the**plank foundation that distributed

**its**weight widely on

**the**Rotunda pavement

**,**supported as it

__is__by ancient brick vaulting.

__Every__dream

**,**

**and**this

__is__true

**of**

**a**mental image

**of**any type even though it may be readily interpreted into

**its**equivalent

**of**wakeful thought

**,**

__is__

**a**psychic phenomenon for which no explanation

__is__available.

__Every__library borrower

**,**or

**at**least those whose taste goes beyond

**the**five-cent fiction rentals

**,**knows what it

__is__to hear

**the**librarian say apologetically

**,**`` I'm sorry

**,**but we don't have that book.

__Every__community

**,**if it

__is__alive has

**a**spirit

**,**

**and**that spirit

__is__

**the**center

**of**

**its**unity

**and**

**identity**.

The restricted principle "

__Every__partially ordered set has**a**maximal totally ordered subset "__is__also equivalent to AC over ZF.__Every__natural-born citizen

**of**

**a**foreign state who

__is__also

**an**American citizen

**and**every natural-born American citizen who

__is__

**a**citizen

**of**

**a**foreign land owes

**a**double allegiance

**,**one to

**the**United States

**,**

**and**one to his homeland

**(**in

**the**event

**of**

**an**immigrant becoming

**a**citizen

**of**

**the**US ), or to his adopted land

**(**in

**the**event

**of**

**an**emigrant natural born citizen

**of**

**the**US becoming

**a**citizen

**of**another nation ).

__Every__line

**of**written text

__is__

**a**mere reflection

**of**references from any

**of**

**a**multitude

**of**traditions

**,**or

**,**as Barthes puts it

**,**"

**the**text

__is__

**a**tissue

**of**quotations drawn from

**the**innumerable centres

**of**culture "; it

__is__never original.

__Every__year

**,**on

**the**last Sunday in April

**,**

**there**

__is__

**an**ice fishing competition in

**the**frozen estuarine waters

**of**

**the**Anadyr River's mouth.

__Every__lattice element

**of**

**the**structure

__is__in

**its**proper place

**,**whether it

__is__

**a**single atom or

**a**molecular grouping.

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