* 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 )

* Every integrable subbundle of the tangent bundle — that is, one whose sections are closed under the Lie bracket — also defines a Lie algebroid.

* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.

* Every holomorphic line bundle on a projective variety is a line bundle of a divisor.

Every vector bundle admits a connection.

Every vector bundle theory ( real, complex etc.

Every minimal projective ruled surface other than the projective plane is the projective bundle of a 2-dimensional vector bundle over some curve.

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 Lie algebra is a Lie algebroid over the one point manifold.

Every compact Lie group G of dimension > 0 has a subgroup isomorphic to the circle group.

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 Little Lie "

Every left-invariant vector field on a Lie group is complete.

Every associative algebra is obviously alternative, but so too are some strictly nonassociative algebras such as the octonions.

Every associative algebra is obviously power-associative, but so are all other alternative algebras ( like the octonions, which are non-associative ) and even some non-alternative algebras like the sedenions.

Every Boolean algebra can be obtained in this way from a suitable topological space: see Stone's representation theorem for Boolean algebras.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

Every six months the presidency rotates between the states, in an order predefined by the Council's members, allowing each state to preside over the body.

Every year many teams from all over Asia converge in Tokyo to compete.

Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.

Every division ring is therefore a division algebra over its center.

Every field is, of course, one-dimensional over its center.

* Every June, Ellensburg hosts Dachshunds on Parade, an event that draws Dachshund dog owners from all over the Northwest.

Every year sidecar racers travel from all over the UK to Knockhill in Scotland to race in the prestigious ' Jock Taylor Memorial Trophy ' race.

Every day, a blessing is recited over the Lulav and the Etrog.

Every major commercial transport and almost every military jet built in the United States over the last 40 years has been tested in this facility.

Every car uses either a 5. 0 L Ford " Boss 302 " SVO or a 5. 0 L Chevrolet small block race-engine ( depending on the make )-capable of producing between 460 and 485 kW ( 620 — 650 bhp ) of power, but generally quoted as a little over 450 kW ( 600 bhp ) in race trim.

* Every finitely-generated commutative algebra over a commutative Noetherian ring is Noetherian.

Every day all over the country, police officers are testifying.

Every character in the novel — both men and women — knows their place, and the traditional stereotypes of gender roles are repeated over and over again.

Every Turing machine computes a certain fixed partial computable function from the input strings over its alphabet.

* Every ninth year, people from all over Sweden assembled at the Temple at Uppsala.

Every year, millions of pilgrims from all over the world come to Częstochowa to see it.

Every Calan Mai, the two would fight over Creiddylad, until a battle on Judgement Day, in which the victor would keep her forever.

Controversy ensued over the use of the phrase " Every seat lost to the government is a seat sold to the Boers " as the Unionists waged a personalised campaign against Liberal critics of the war – some posters even portrayed Liberal MPs praising President Kruger and helping him to haul down the Union Jack.

Every year, the post office also creates a special Christmas hand-cancellation pictorial postmark for use during December, which also attracts mail from all over the world.

A quotation attributed to Kolmogorov is into English: " Every mathematician believes that he is ahead over all others.

Every August the Mountain Mama Road Bike Challenge brings cyclists from all over the country to challenge themselves on the steep roads of Highland County.

The argument over the quality of Fitzgerald ’ s translation of the Rubaiyat has, according to Dougan, diverted attention from a fuller understanding of the deeply esoteric message contained in Omar ’ s actual material – " Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature ".