Noun phrase
/ˈæb.sə.luːt.li ɪ.rɪˈdjuː.sə.bəl ˈkær.ɪk.tər/
The term "absolutely irreducible character" is primarily used in the context of representation theory in mathematics, particularly in group theory. An absolutely irreducible character is a character that cannot be decomposed into a direct sum of other characters over the field of complex numbers. This term is technical and is often found in written mathematical contexts rather than in everyday speech.
This phrase is specialized and is not commonly used in everyday conversation. It appears predominantly in academic papers, journals, and textbooks related to algebra and representation theory.
The absolutely irreducible character of a group G helps us understand its representation theory more deeply.
(La característica absolutamente irreducible de un grupo G nos ayuda a entender más a fondo su teoría de representación.)
In representation theory, studying the absolutely irreducible character can yield important insights into the structure of the group.
(En la teoría de representación, estudiar la característica absolutamente irreducible puede ofrecer importantes perspectivas sobre la estructura del grupo.)
Researchers have discovered new properties related to the absolutely irreducible character, advancing the field significantly.
(Los investigadores han descubierto nuevas propiedades relacionadas con la característica absolutamente irreducible, avanzando significativamente en el campo.)
Although the phrase "absolutely irreducible character" is not commonly found in idiomatic expressions, the concept of being "irreducible" is often used in different contexts. Here are some idioms that incorporate "irreducible":
The truth is sometimes an irreducible fact that we cannot ignore.
(La verdad es a veces un hecho irreducible que no podemos ignorar.)
In debates, emotions can be irreducible, influencing people more than logic.
(En los debates, las emociones pueden ser irreducibles, influyendo a las personas más que la lógica.)
The irreducible complexity of the problem makes it challenging to solve.
(La complejidad irreducible del problema lo hace difícil de resolver.)
The term "irreducible" comes from the Latin word "reducere," meaning "to bring back.” The prefix "in-" negates the term, so it literally means "not able to be brought back" or "not capable of being reduced." The word "character" comes from the Greek "kharaktēr," meaning "a stamping tool or mark."