This preprint supersedes the previous version, which was only about Kontsevich's conjecture on relation between monodromy of a family (weakly) CY varieties and action cohomology group autoequivalences derived category in mirror dual family. Here we add another autoequivalence variety its Neron-Severi Lie algebra.

We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.

Comparing the bounded derived categories of an algebra and endomorphism a given support {\tau}-tilting module, we find relation between dimensions module.

The word, Boolean, was derived from the name of a British mathematician, George Boole, as a result of his classical work on logic. Boolean algebra can be defined as a set, whose members have two possible values, with two binary operators and one unary operator, satisfying the properties of commutativity, associativity, distributivity, existence of identity and complement. Boolean algebra has im...

It is proved that for a ring R either an affine algebra over field, or equicharacteristic complete local ring, some power of the Jacobian ideal annihilates ExtRd+1(−,−), where d Krull dimension R. Sufficient conditions are identified under which itself these Ext-modules, and examples provided show this not always case. The crucial new idea to consider derived version Noether different algebra.

We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of finite characteristic with a given (generalized) regular central character are the same as coherent sheaves on the formal neighborhood of the corresponding (generalized) Springer fiber. The first step is to observe that the derived functor of global sections provi...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

We consider the lower central filtration of the free associative algebra An with n generators as a Lie algebra. We consider the associated graded Lie algebra. It is shown that this Lie algebra has a huge center which belongs to the cyclic words, and on the quotient Lie algebra by the center there acts the Lie algebraWn of polynomial vector fields on C. We compute the space [An, An]/[An, [An, An...