In abstract algebra, a Valya algebra (or Valentina algebra) is a nonassociative algebra "M" over a field "F" whose multiplicative binary operation "g" satisfies the following axioms:
1. The skew-symmetry condition 
formula_1 
for all formula_2. 
2. The Valya identity 
formula_3
for all formula_4, where k=1,2...,6, and
formula_5
3. The bilinear condition
formula_6
for all formula_7 and formula_8. 
We say that M is a Valya algebra if the commutant of this algebra is a Lie subalgebra. Each Lie algebra is a Valya algebra. 
There is the following relationship between the commutant-associative algebra and Valentina algebra. The replacement of the multiplication g(A,B) in an algebra M by the operation of commutation [A,B]=g(A,B)-g(B,A), makes it into the algebra formula_9. 
If M is a commutant-associative algebra, then formula_9 is a Valya algebra. A Valya algebra is a generalization of a Lie algebra.
Examples.
Let us give the following examples regarding Valya algebras.
(1) Every finite Valya algebra is the tangent algebra of an analytic local commutant-associative loop (Valya loop) as each finite Lie algebra is the tangent algebra of an analytic local group (Lie group). This is the analog of the classical correspondence between analytic local groups (Lie groups) and Lie algebras.
(2) A bilinear operation for the differential 1-forms
formula_11
on a symplectic manifold can be introduced by the rule
 formula_12
where formula_13 is 1-form. A set of all nonclosed 1-forms, together with this operation, is Lie algebra.
If formula_14 and formula_15 are closed 1-forms, then 
formula_16 and
 formula_17
A set of all closed 1-forms, together with this bracket, form a Lie algebra. A set of all nonclosed 1-forms together with the bilinear operation formula_13 is a Valya algebra, and it is not a Lie algebra.