Klaster Cebirlerinin Mütasyon Sınıfları

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TVRZMU5qWTI.pdf

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2016

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Seven, Ahmet İrfan

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Klaster cebirleri (cluster algebras) önce matematiğin klasik bir alanı olan temsil teorisinde ortaya çıkmış ve daha sonra varlığı diğer farklı alanlarda da farkedilmiş bir matematiksel yapıdır. Bu projede, klaster cebirlerini belirleyen mütasyon sınıflarının temel cebirselkombinatoryal özellikleri ortaya çıkarılmıştır. Bu kapsamda, matematiğin temel objelerinden olan Kac-Moody Lie cebirlerine karşılık gelen klaster cebirleri ile çeşitli sonlu mütasyon tipine sahip klaster cebirleri için mütasyon değişmezleri elde edilmiştir. Elde edilen sonuçlar, bu konular arasında yeni bağlantılar ortaya çıkarmış ve daha iyi anlaşılmalarına katkıda bulunmuştur. Projede elde edilen sonuç ve araçlar klaster cebirleri ile ilgili açık hesaplamalar yapmaya imkan vermektedir. Bu yönüyle proje, klaster cebirleri teorisinde önemli bir boşluğu doldurmuştur. Projede elde edilen sonuçlar dört makale olarak yazılmış ve çeşitli uluslararası bilimsel toplantılarda sunulmuştur.

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https://app.trdizin.gov.tr/publication/project/detail/TVRZMU5qWTI
https://hdl.handle.net/11511/50266

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Citation Formats

A. İ. Seven, “Klaster Cebirlerinin Mütasyon Sınıfları,” 2016. Accessed: 00, 2020. [Online]. Available: https://app.trdizin.gov.tr/publication/project/detail/TVRZMU5qWTI.