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Τι (ποιος) είναι lowest weight vector - ορισμός
CONCEPT IN LIE-ALGEBRA REPRESENTATION THEORY
Weight (Lie algebra); Lowest weight representation; Highest weight representation; Weight lattice; Weight (Lie algebras); Highest weight; Lowest weight; Highest weight module; Weight vector; Weight module; Highest weight modules; Fundamental weight; Highest weight vector; Weight modules; Dominant weight; Integral weight; Fundamental Weyl chamber; Simple highest weight module; Simultaneous eigenvector; Highest-weight module; Weight diagram; Weight spaces; Weight subspace; Coweight; Weight space (representation theory); Highest-weight representation
free vector
GEOMETRIC OBJECT THAT HAS MAGNITUDE (OR LENGTH) AND DIRECTION
Vector (classical mechanics); Three-vector; Vector sum; Vector addition; Spatial vector; Vector (physics); Vector subtraction; Relative vector; Spacial vector; Physical vector; Vector methods (physics); Vector component; Component (vector); Bound vector; Vector (spatial); Vector (geometry); Free vector; Vector (geometric); Triangle law; Euclidean vectors; Vector direction; Vector components; 3d vector; Euclid vector; 3D vector; Geometric vector; Magnitude of resultant vector; Euclidian vector; Vector quantity; Resultant vector; Antiparallel vectors
¦ noun Mathematics a vector of which only the magnitude and direction are specified, not the position or line of action.
weigh
![Ancient Greek]] official bronze weights dating from around the 6th century BC, exhibited in the [[Ancient Agora Museum]] in Athens, housed in the [[Stoa of Attalus]].](https://commons.wikimedia.org/wiki/Special:FilePath/3199 - Athens - Stoà of Attalus Museum - Bronze weights - Photo by Giovanni Dall'Orto, Nov 9 2009.jpg?width=200 "Ancient Greek]] official bronze weights dating from around the 6th century BC, exhibited in the [[Ancient Agora Museum]] in Athens, housed in the [[Stoa of Attalus]].")
![0}} in 0.86 seconds. This is a horizontal acceleration of 5.3{{spaces}}g. Combined with the vertical g-force in the stationary case the [[Pythagorean theorem]] yields a g-force of 5.4{{spaces}}g. It is this g-force that causes the driver's weight if one uses the operational definition. If one uses the gravitational definition, the driver's weight is unchanged by the motion of the car.](https://commons.wikimedia.org/wiki/Special:FilePath/Nitrolympics TopFuel 2005.jpg?width=200 "0}} in 0.86 seconds. This is a horizontal acceleration of 5.3{{spaces}}g. Combined with the vertical g-force in the stationary case the [[Pythagorean theorem]] yields a g-force of 5.4{{spaces}}g. It is this g-force that causes the driver's weight if one uses the operational definition. If one uses the gravitational definition, the driver's weight is unchanged by the motion of the car.")
![A [[weighbridge]], used for weighing trucks](https://commons.wikimedia.org/wiki/Special:FilePath/Peso-Valdivia-dsc02545.jpg?width=200 "A [[weighbridge]], used for weighing trucks")
![moments]] acting on it sum to zero).](https://commons.wikimedia.org/wiki/Special:FilePath/WeightNormal.svg?width=200 "moments]] acting on it sum to zero).")
FORCE ACTING ON A MASS DUE TO GRAVITY
Gross weight; Measure of weight; Weigh; Net weight; Nett weight; Weighty; Weighing; Ponderous; Gross rail load; Laden weight; Units of weight; Wieght; Heaviness
v.
1) to weigh heavily
2) (d; intr.) ('to count') to weigh against (his testimony will weigh heavily against you)
3) (d; tr.) ('to balance') to weigh against (to weigh one argument against another)
4) (d; intr.) ('to press') to weigh on (legal problems weighed heavily on her mind)
5) (P; intr.) ('to have a weight') the suitcase weighs quite a lot
weight
FORCE ACTING ON A MASS DUE TO GRAVITY
Gross weight; Measure of weight; Weigh; Net weight; Nett weight; Weighty; Weighing; Ponderous; Gross rail load; Laden weight; Units of weight; Wieght; Heaviness
I
n.
amount weighed, heaviness
1) to gain, put on weight
2) to lose, take off weight
3) dead; gross; minimum; net weight
4) atomic; avoirdupois; birth; molecular weight
5) under a weight (the table collapsed under the weight of the food)
device used for its heaviness in athletic exercises
6) to lift weights
7) heavy; light weights
8) a set of weights
importance
9) to carry weight
10) to add; attach, give, lend weight to
11) considerable weight
12) (misc.) to throw one's weight around/about (BE) ('to flaunt one's influence'); to pull one's weight ('to do one's fair share')
II
v. (D; tr.) ('to slant') to weight against (the evidence was weighted against me)
Βικιπαίδεια
Weight (representation theory)
In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space.
